rint 0.1.1

/// A generator of evaluation points for a fully-symmetric integration rule.
///
/// A fully-symmetric integration rule is one in which all points which can be created from a base
/// point by negation and permutation are used to evaluate the function with the same weight. The
/// [`Generator`] can be used to generate these evaluation points through the
/// [`Generator::permutations`] and [`Generator::point_permutations`] methods.
#[derive(Debug, Clone, PartialEq, PartialOrd)]
pub(crate) struct Generator<const N: usize>([f64; N]);

impl<const N: usize> Generator<N> {
    pub(crate) const fn new(input: [f64; N]) -> Self {
        Self(input)
    }

    pub(crate) const fn generator(&self) -> &[f64; N] {
        &self.0
    }

    pub(crate) const fn point(&self, centre: &[f64; N], half_widths: &[f64; N]) -> [f64; N] {
        let mut point = [0.0; N];
        let mut i = 0;
        while i < N {
            point[i] = centre[i] + self.0[i] * half_widths[i];
            i += 1;
        }
        point
    }

    #[cfg(test)]
    pub(crate) const fn permutations(&self) -> Permutations<N> {
        Permutations::new(self.generator())
    }

    pub(crate) const fn point_permutations(
        &self,
        centre: &[f64; N],
        half_widths: &[f64; N],
    ) -> Permutations<N> {
        Permutations::new(self.generator())
            .with_centre(centre)
            .with_half_widths(half_widths)
    }
}

/// An iterator over the evaluation points produced from a base [`Generator`]
pub(crate) struct Permutations<const N: usize> {
    initial: bool,
    current: [f64; N],
    j_exchange: usize,
    i_exchange: usize,
    centre: [f64; N],
    half_widths: [f64; N],
}

impl<const N: usize> Permutations<N> {
    pub(crate) const fn new(first: &[f64; N]) -> Self {
        Self {
            initial: true,
            current: *first,
            j_exchange: 0,
            i_exchange: 0,
            centre: [0.0; N],
            half_widths: [1.0; N],
        }
    }

    pub(crate) const fn with_centre(mut self, centre: &[f64; N]) -> Self {
        self.centre = *centre;
        self
    }

    pub(crate) const fn with_half_widths(mut self, half_widths: &[f64; N]) -> Self {
        self.half_widths = *half_widths;
        self
    }

    const fn point(&self) -> [f64; N] {
        let mut output = [0.0; N];
        let mut i = 0;
        while i < N {
            output[i] = self.centre[i] + self.current[i] * self.half_widths[i];
            i += 1;
        }
        output
    }
}

impl<const N: usize> Iterator for Permutations<N> {
    type Item = [f64; N];

    fn next(&mut self) -> Option<Self::Item> {
        if self.initial {
            self.initial = false;
            return Some(self.point());
        }

        for i in 0..N {
            self.current[i] = -self.current[i];
            if self.current[i] < 0.0 {
                return Some(self.point());
            }
        }

        for i in 1..N {
            if self.current[i - 1] > self.current[i] {
                let value_i = self.current[i];
                self.i_exchange = i - 1;
                for j in 1..=(i / 2) {
                    let value_j = self.current[j - 1];
                    self.current.swap(j - 1, i - j);
                    if value_j <= value_i {
                        self.i_exchange -= 1;
                    }
                    if self.current[j - 1] > value_i {
                        self.j_exchange = j - 1;
                    }
                }
                if self.current[self.i_exchange] <= value_i {
                    self.i_exchange = self.j_exchange;
                }
                self.current[i] = self.current[self.i_exchange];
                self.current[self.i_exchange] = value_i;
                return Some(self.point());
            }
        }

        None
    }
}

#[cfg(test)]
#[allow(clippy::too_many_lines)]
mod tests_no_centre_or_half_widths {
    use super::*;

    #[test]
    fn check_ndim_2_generators() {
        let ndim = 2;

        {
            let vv = Generator::new([0.75f64, 0.75]);

            let should_be = [[0.75, 0.75], [-0.75, 0.75], [0.75, -0.75], [-0.75, -0.75]].iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2usize.pow(ndim));
        }

        {
            let vv = Generator::new([0.75f64, 0.5]);

            let should_be = [
                [0.75, 0.5],
                [-0.75, 0.5],
                [0.75, -0.5],
                [-0.75, -0.5],
                [0.5, 0.75],
                [-0.5, 0.75],
                [0.5, -0.75],
                [-0.5, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0]);

            let should_be = [
                [0.75f64, 0.0],
                [-0.75f64, 0.0],
                [0.0, 0.75f64],
                [0.0, -0.75f64],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim);
        }
    }

    #[test]
    fn check_ndim_3_generators() {
        let ndim = 3;

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75],
                [0.75, 0.75, 0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2usize.pow(ndim));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5]);

            let should_be = [
                [0.75, 0.75, 0.5],
                [-0.75, 0.75, 0.5],
                [0.75, -0.75, 0.5],
                [-0.75, -0.75, 0.5],
                [0.75, 0.75, -0.5],
                [-0.75, 0.75, -0.5],
                [0.75, -0.75, -0.5],
                [-0.75, -0.75, -0.5],
                [0.75, 0.5, 0.75],
                [-0.75, 0.5, 0.75],
                [0.75, -0.5, 0.75],
                [-0.75, -0.5, 0.75],
                [0.75, 0.5, -0.75],
                [-0.75, 0.5, -0.75],
                [0.75, -0.5, -0.75],
                [-0.75, -0.5, -0.75],
                [0.5, 0.75, 0.75],
                [-0.5, 0.75, 0.75],
                [0.5, -0.75, 0.75],
                [-0.5, -0.75, 0.75],
                [0.5, 0.75, -0.75],
                [-0.5, 0.75, -0.75],
                [0.5, -0.75, -0.75],
                [-0.5, -0.75, -0.75],
                [0.75, 0.75, 0.5],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0]);

            let should_be = [
                [0.75f64, 0.5, 0.0],
                [-0.75f64, 0.5, 0.0],
                [0.75f64, -0.5, 0.0],
                [-0.75f64, -0.5, 0.0],
                [0.5, 0.75f64, 0.0],
                [-0.5, 0.75f64, 0.0],
                [0.5, -0.75f64, 0.0],
                [-0.5, -0.75f64, 0.0],
                [0.75f64, 0.0, 0.5],
                [-0.75f64, 0.0, 0.5],
                [0.75f64, 0.0, -0.5],
                [-0.75f64, 0.0, -0.5],
                [0.0, 0.75f64, 0.5],
                [0.0, -0.75f64, 0.5],
                [0.0, 0.75f64, -0.5],
                [0.0, -0.75f64, -0.5],
                [0.5, 0.0, 0.75f64],
                [-0.5, 0.0, 0.75f64],
                [0.5, 0.0, -0.75f64],
                [-0.5, 0.0, -0.75f64],
                [0.0, 0.5, 0.75f64],
                [0.0, -0.5, 0.75f64],
                [0.0, 0.5, -0.75f64],
                [0.0, -0.5, -0.75f64],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0]);

            let should_be = [
                [0.75f64, 0.75, 0.0],
                [-0.75f64, 0.75, 0.0],
                [0.75f64, -0.75, 0.0],
                [-0.75f64, -0.75, 0.0],
                [0.75f64, 0.0, 0.75],
                [-0.75f64, 0.0, 0.75],
                [0.75f64, 0.0, -0.75],
                [-0.75f64, 0.0, -0.75],
                [0.0, 0.75f64, 0.75],
                [0.0, -0.75f64, 0.75],
                [0.0, 0.75f64, -0.75],
                [0.0, -0.75f64, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0]);

            let should_be = [
                [0.75f64, 0.0, 0.0],
                [-0.75f64, 0.0, 0.0],
                [0.0, 0.75f64, 0.0],
                [0.0, -0.75f64, 0.0],
                [0.0, 0.0, 0.75],
                [0.0, -0.0, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim);
        }
    }

    #[test]
    fn check_ndim_4_generators() {
        let ndim = 4;

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2usize.pow(ndim));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.0],
                [-0.75, 0.75, 0.75, 0.0],
                [0.75, -0.75, 0.75, 0.0],
                [-0.75, -0.75, 0.75, 0.0],
                [0.75, 0.75, -0.75, 0.0],
                [-0.75, 0.75, -0.75, 0.0],
                [0.75, -0.75, -0.75, 0.0],
                [-0.75, -0.75, -0.75, 0.0],
                [0.75, 0.75, -0.0, 0.75],
                [-0.75, 0.75, -0.0, 0.75],
                [0.75, -0.75, -0.0, 0.75],
                [-0.75, -0.75, -0.0, 0.75],
                [0.75, 0.75, 0.0, -0.75],
                [-0.75, 0.75, 0.0, -0.75],
                [0.75, -0.75, 0.0, -0.75],
                [-0.75, -0.75, 0.0, -0.75],
                [0.75, -0.0, 0.75, 0.75],
                [-0.75, -0.0, 0.75, 0.75],
                [0.75, 0.0, -0.75, 0.75],
                [-0.75, 0.0, -0.75, 0.75],
                [0.75, -0.0, 0.75, -0.75],
                [-0.75, -0.0, 0.75, -0.75],
                [0.75, 0.0, -0.75, -0.75],
                [-0.75, 0.0, -0.75, -0.75],
                [-0.0, 0.75, 0.75, 0.75],
                [0.0, -0.75, 0.75, 0.75],
                [-0.0, 0.75, -0.75, 0.75],
                [0.0, -0.75, -0.75, 0.75],
                [-0.0, 0.75, 0.75, -0.75],
                [0.0, -0.75, 0.75, -0.75],
                [-0.0, 0.75, -0.75, -0.75],
                [0.0, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2) / 3);
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.50, 0.0],
                [-0.75, 0.75, 0.50, 0.0],
                [0.75, -0.75, 0.50, 0.0],
                [-0.75, -0.75, 0.50, 0.0],
                [0.75, 0.75, -0.50, 0.0],
                [-0.75, 0.75, -0.50, 0.0],
                [0.75, -0.75, -0.50, 0.0],
                [-0.75, -0.75, -0.50, 0.0],
                [0.75, 0.50, 0.75, -0.0],
                [-0.75, 0.50, 0.75, -0.0],
                [0.75, -0.50, 0.75, -0.0],
                [-0.75, -0.50, 0.75, -0.0],
                [0.75, 0.50, -0.75, -0.0],
                [-0.75, 0.50, -0.75, -0.0],
                [0.75, -0.50, -0.75, -0.0],
                [-0.75, -0.50, -0.75, -0.0],
                [0.50, 0.75, 0.75, 0.0],
                [-0.50, 0.75, 0.75, 0.0],
                [0.50, -0.75, 0.75, 0.0],
                [-0.50, -0.75, 0.75, 0.0],
                [0.50, 0.75, -0.75, 0.0],
                [-0.50, 0.75, -0.75, 0.0],
                [0.50, -0.75, -0.75, 0.0],
                [-0.50, -0.75, -0.75, 0.0],
                [0.75, 0.75, -0.0, 0.50],
                [-0.75, 0.75, -0.0, 0.50],
                [0.75, -0.75, -0.0, 0.50],
                [-0.75, -0.75, -0.0, 0.50],
                [0.75, 0.75, 0.0, -0.50],
                [-0.75, 0.75, 0.0, -0.50],
                [0.75, -0.75, 0.0, -0.50],
                [-0.75, -0.75, 0.0, -0.50],
                [0.75, -0.0, 0.75, 0.50],
                [-0.75, -0.0, 0.75, 0.50],
                [0.75, 0.0, -0.75, 0.50],
                [-0.75, 0.0, -0.75, 0.50],
                [0.75, -0.0, 0.75, -0.50],
                [-0.75, -0.0, 0.75, -0.50],
                [0.75, 0.0, -0.75, -0.50],
                [-0.75, 0.0, -0.75, -0.50],
                [-0.0, 0.75, 0.75, 0.50],
                [0.0, -0.75, 0.75, 0.50],
                [-0.0, 0.75, -0.75, 0.50],
                [0.0, -0.75, -0.75, 0.50],
                [-0.0, 0.75, 0.75, -0.50],
                [0.0, -0.75, 0.75, -0.50],
                [-0.0, 0.75, -0.75, -0.50],
                [0.0, -0.75, -0.75, -0.50],
                [0.75, 0.50, -0.0, 0.75],
                [-0.75, 0.50, -0.0, 0.75],
                [0.75, -0.50, -0.0, 0.75],
                [-0.75, -0.50, -0.0, 0.75],
                [0.75, 0.50, 0.0, -0.75],
                [-0.75, 0.50, 0.0, -0.75],
                [0.75, -0.50, 0.0, -0.75],
                [-0.75, -0.50, 0.0, -0.75],
                [0.50, 0.75, -0.0, 0.75],
                [-0.50, 0.75, -0.0, 0.75],
                [0.50, -0.75, -0.0, 0.75],
                [-0.50, -0.75, -0.0, 0.75],
                [0.50, 0.75, 0.0, -0.75],
                [-0.50, 0.75, 0.0, -0.75],
                [0.50, -0.75, 0.0, -0.75],
                [-0.50, -0.75, 0.0, -0.75],
                [0.75, -0.0, 0.50, 0.75],
                [-0.75, -0.0, 0.50, 0.75],
                [0.75, 0.0, -0.50, 0.75],
                [-0.75, 0.0, -0.50, 0.75],
                [0.75, -0.0, 0.50, -0.75],
                [-0.75, -0.0, 0.50, -0.75],
                [0.75, 0.0, -0.50, -0.75],
                [-0.75, 0.0, -0.50, -0.75],
                [-0.0, 0.75, 0.50, 0.75],
                [0.0, -0.75, 0.50, 0.75],
                [-0.0, 0.75, -0.50, 0.75],
                [0.0, -0.75, -0.50, 0.75],
                [-0.0, 0.75, 0.50, -0.75],
                [0.0, -0.75, 0.50, -0.75],
                [-0.0, 0.75, -0.50, -0.75],
                [0.0, -0.75, -0.50, -0.75],
                [0.50, -0.0, 0.75, 0.75],
                [-0.50, -0.0, 0.75, 0.75],
                [0.50, 0.0, -0.75, 0.75],
                [-0.50, 0.0, -0.75, 0.75],
                [0.50, -0.0, 0.75, -0.75],
                [-0.50, -0.0, 0.75, -0.75],
                [0.50, 0.0, -0.75, -0.75],
                [-0.50, 0.0, -0.75, -0.75],
                [-0.0, 0.50, 0.75, 0.75],
                [0.0, -0.50, 0.75, 0.75],
                [-0.0, 0.50, -0.75, 0.75],
                [0.0, -0.50, -0.75, 0.75],
                [-0.0, 0.50, 0.75, -0.75],
                [0.0, -0.50, 0.75, -0.75],
                [-0.0, 0.50, -0.75, -0.75],
                [0.0, -0.50, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.50, 0.0, 0.0],
                [-0.75, 0.50, 0.0, 0.0],
                [0.75, -0.50, 0.0, 0.0],
                [-0.75, -0.50, 0.0, 0.0],
                [0.50, 0.75, -0.0, -0.0],
                [-0.50, 0.75, -0.0, -0.0],
                [0.50, -0.75, -0.0, -0.0],
                [-0.50, -0.75, -0.0, -0.0],
                [0.75, 0.0, 0.50, 0.0],
                [-0.75, 0.0, 0.50, 0.0],
                [0.75, -0.0, -0.50, 0.0],
                [-0.75, -0.0, -0.50, 0.0],
                [0.0, 0.75, 0.50, -0.0],
                [-0.0, -0.75, 0.50, -0.0],
                [0.0, 0.75, -0.50, -0.0],
                [-0.0, -0.75, -0.50, -0.0],
                [0.50, 0.0, 0.75, 0.0],
                [-0.50, 0.0, 0.75, 0.0],
                [0.50, -0.0, -0.75, 0.0],
                [-0.50, -0.0, -0.75, 0.0],
                [0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.50, 0.75, -0.0],
                [0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.50, -0.75, -0.0],
                [0.75, 0.0, 0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.50],
                [0.75, -0.0, -0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.50],
                [0.0, 0.75, 0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.50],
                [0.0, 0.75, -0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.50],
                [0.0, 0.0, 0.75, 0.50],
                [-0.0, -0.0, -0.75, 0.50],
                [0.0, 0.0, 0.75, -0.50],
                [-0.0, -0.0, -0.75, -0.50],
                [0.50, 0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.0, 0.75],
                [0.50, -0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.0, -0.75],
                [0.0, 0.50, 0.0, 0.75],
                [-0.0, -0.50, 0.0, 0.75],
                [0.0, 0.50, -0.0, -0.75],
                [-0.0, -0.50, -0.0, -0.75],
                [0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.0, -0.50, 0.75],
                [0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.0, -0.50, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.0, 0.0],
                [-0.75, 0.75, 0.0, 0.0],
                [0.75, -0.75, 0.0, 0.0],
                [-0.75, -0.75, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.0],
                [-0.75, -0.0, 0.75, -0.0],
                [0.75, 0.0, -0.75, -0.0],
                [-0.75, 0.0, -0.75, -0.0],
                [-0.0, 0.75, 0.75, 0.0],
                [0.0, -0.75, 0.75, 0.0],
                [-0.0, 0.75, -0.75, 0.0],
                [0.0, -0.75, -0.75, 0.0],
                [0.75, -0.0, -0.0, 0.75],
                [-0.75, -0.0, -0.0, 0.75],
                [0.75, 0.0, 0.0, -0.75],
                [-0.75, 0.0, 0.0, -0.75],
                [-0.0, 0.75, -0.0, 0.75],
                [0.0, -0.75, -0.0, 0.75],
                [-0.0, 0.75, 0.0, -0.75],
                [0.0, -0.75, 0.0, -0.75],
                [-0.0, -0.0, 0.75, 0.75],
                [0.0, 0.0, -0.75, 0.75],
                [-0.0, -0.0, 0.75, -0.75],
                [0.0, 0.0, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.0, -0.0],
                [0.0, -0.75, -0.0, -0.0],
                [0.0, -0.0, 0.75, 0.0],
                [-0.0, 0.0, -0.75, 0.0],
                [-0.0, -0.0, 0.0, 0.75],
                [0.0, 0.0, -0.0, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim);
        }
    }

    #[test]
    fn check_ndim_5_generators() {
        let ndim = 5;

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, 0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2usize.pow(ndim));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.0, 0.0],
                [-0.75, 0.75, 0.75, 0.0, 0.0],
                [0.75, -0.75, 0.75, 0.0, 0.0],
                [-0.75, -0.75, 0.75, 0.0, 0.0],
                [0.75, 0.75, -0.75, 0.0, 0.0],
                [-0.75, 0.75, -0.75, 0.0, 0.0],
                [0.75, -0.75, -0.75, 0.0, 0.0],
                [-0.75, -0.75, -0.75, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.75, -0.0],
                [-0.75, 0.75, -0.0, 0.75, -0.0],
                [0.75, -0.75, -0.0, 0.75, -0.0],
                [-0.75, -0.75, -0.0, 0.75, -0.0],
                [0.75, 0.75, 0.0, -0.75, -0.0],
                [-0.75, 0.75, 0.0, -0.75, -0.0],
                [0.75, -0.75, 0.0, -0.75, -0.0],
                [-0.75, -0.75, 0.0, -0.75, -0.0],
                [0.75, -0.0, 0.75, 0.75, 0.0],
                [-0.75, -0.0, 0.75, 0.75, 0.0],
                [0.75, 0.0, -0.75, 0.75, 0.0],
                [-0.75, 0.0, -0.75, 0.75, 0.0],
                [0.75, -0.0, 0.75, -0.75, 0.0],
                [-0.75, -0.0, 0.75, -0.75, 0.0],
                [0.75, 0.0, -0.75, -0.75, 0.0],
                [-0.75, 0.0, -0.75, -0.75, 0.0],
                [-0.0, 0.75, 0.75, 0.75, -0.0],
                [0.0, -0.75, 0.75, 0.75, -0.0],
                [-0.0, 0.75, -0.75, 0.75, -0.0],
                [0.0, -0.75, -0.75, 0.75, -0.0],
                [-0.0, 0.75, 0.75, -0.75, -0.0],
                [0.0, -0.75, 0.75, -0.75, -0.0],
                [-0.0, 0.75, -0.75, -0.75, -0.0],
                [0.0, -0.75, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.75],
                [-0.75, 0.75, 0.0, -0.0, 0.75],
                [0.75, -0.75, 0.0, -0.0, 0.75],
                [-0.75, -0.75, 0.0, -0.0, 0.75],
                [0.75, 0.75, -0.0, 0.0, -0.75],
                [-0.75, 0.75, -0.0, 0.0, -0.75],
                [0.75, -0.75, -0.0, 0.0, -0.75],
                [-0.75, -0.75, -0.0, 0.0, -0.75],
                [0.75, 0.0, 0.75, -0.0, 0.75],
                [-0.75, 0.0, 0.75, -0.0, 0.75],
                [0.75, -0.0, -0.75, -0.0, 0.75],
                [-0.75, -0.0, -0.75, -0.0, 0.75],
                [0.75, 0.0, 0.75, 0.0, -0.75],
                [-0.75, 0.0, 0.75, 0.0, -0.75],
                [0.75, -0.0, -0.75, 0.0, -0.75],
                [-0.75, -0.0, -0.75, 0.0, -0.75],
                [0.0, 0.75, 0.75, -0.0, 0.75],
                [-0.0, -0.75, 0.75, -0.0, 0.75],
                [0.0, 0.75, -0.75, -0.0, 0.75],
                [-0.0, -0.75, -0.75, -0.0, 0.75],
                [0.0, 0.75, 0.75, 0.0, -0.75],
                [-0.0, -0.75, 0.75, 0.0, -0.75],
                [0.0, 0.75, -0.75, 0.0, -0.75],
                [-0.0, -0.75, -0.75, 0.0, -0.75],
                [0.75, -0.0, 0.0, 0.75, 0.75],
                [-0.75, -0.0, 0.0, 0.75, 0.75],
                [0.75, 0.0, -0.0, -0.75, 0.75],
                [-0.75, 0.0, -0.0, -0.75, 0.75],
                [0.75, -0.0, 0.0, 0.75, -0.75],
                [-0.75, -0.0, 0.0, 0.75, -0.75],
                [0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.0, 0.75, 0.0, 0.75, 0.75],
                [0.0, -0.75, 0.0, 0.75, 0.75],
                [-0.0, 0.75, -0.0, -0.75, 0.75],
                [0.0, -0.75, -0.0, -0.75, 0.75],
                [-0.0, 0.75, 0.0, 0.75, -0.75],
                [0.0, -0.75, 0.0, 0.75, -0.75],
                [-0.0, 0.75, -0.0, -0.75, -0.75],
                [0.0, -0.75, -0.0, -0.75, -0.75],
                [0.0, -0.0, 0.75, 0.75, 0.75],
                [-0.0, 0.0, -0.75, 0.75, 0.75],
                [0.0, -0.0, 0.75, -0.75, 0.75],
                [-0.0, 0.0, -0.75, -0.75, 0.75],
                [0.0, -0.0, 0.75, 0.75, -0.75],
                [-0.0, 0.0, -0.75, 0.75, -0.75],
                [0.0, -0.0, 0.75, -0.75, -0.75],
                [-0.0, 0.0, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2) / 3);
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.50, 0.0, 0.0],
                [-0.75, 0.75, 0.50, 0.0, 0.0],
                [0.75, -0.75, 0.50, 0.0, 0.0],
                [-0.75, -0.75, 0.50, 0.0, 0.0],
                [0.75, 0.75, -0.50, 0.0, 0.0],
                [-0.75, 0.75, -0.50, 0.0, 0.0],
                [0.75, -0.75, -0.50, 0.0, 0.0],
                [-0.75, -0.75, -0.50, 0.0, 0.0],
                [0.75, 0.50, 0.75, -0.0, -0.0],
                [-0.75, 0.50, 0.75, -0.0, -0.0],
                [0.75, -0.50, 0.75, -0.0, -0.0],
                [-0.75, -0.50, 0.75, -0.0, -0.0],
                [0.75, 0.50, -0.75, -0.0, -0.0],
                [-0.75, 0.50, -0.75, -0.0, -0.0],
                [0.75, -0.50, -0.75, -0.0, -0.0],
                [-0.75, -0.50, -0.75, -0.0, -0.0],
                [0.50, 0.75, 0.75, 0.0, 0.0],
                [-0.50, 0.75, 0.75, 0.0, 0.0],
                [0.50, -0.75, 0.75, 0.0, 0.0],
                [-0.50, -0.75, 0.75, 0.0, 0.0],
                [0.50, 0.75, -0.75, 0.0, 0.0],
                [-0.50, 0.75, -0.75, 0.0, 0.0],
                [0.50, -0.75, -0.75, 0.0, 0.0],
                [-0.50, -0.75, -0.75, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.50, -0.0],
                [-0.75, 0.75, -0.0, 0.50, -0.0],
                [0.75, -0.75, -0.0, 0.50, -0.0],
                [-0.75, -0.75, -0.0, 0.50, -0.0],
                [0.75, 0.75, 0.0, -0.50, -0.0],
                [-0.75, 0.75, 0.0, -0.50, -0.0],
                [0.75, -0.75, 0.0, -0.50, -0.0],
                [-0.75, -0.75, 0.0, -0.50, -0.0],
                [0.75, -0.0, 0.75, 0.50, 0.0],
                [-0.75, -0.0, 0.75, 0.50, 0.0],
                [0.75, 0.0, -0.75, 0.50, 0.0],
                [-0.75, 0.0, -0.75, 0.50, 0.0],
                [0.75, -0.0, 0.75, -0.50, 0.0],
                [-0.75, -0.0, 0.75, -0.50, 0.0],
                [0.75, 0.0, -0.75, -0.50, 0.0],
                [-0.75, 0.0, -0.75, -0.50, 0.0],
                [-0.0, 0.75, 0.75, 0.50, -0.0],
                [0.0, -0.75, 0.75, 0.50, -0.0],
                [-0.0, 0.75, -0.75, 0.50, -0.0],
                [0.0, -0.75, -0.75, 0.50, -0.0],
                [-0.0, 0.75, 0.75, -0.50, -0.0],
                [0.0, -0.75, 0.75, -0.50, -0.0],
                [-0.0, 0.75, -0.75, -0.50, -0.0],
                [0.0, -0.75, -0.75, -0.50, -0.0],
                [0.75, 0.50, -0.0, 0.75, 0.0],
                [-0.75, 0.50, -0.0, 0.75, 0.0],
                [0.75, -0.50, -0.0, 0.75, 0.0],
                [-0.75, -0.50, -0.0, 0.75, 0.0],
                [0.75, 0.50, 0.0, -0.75, 0.0],
                [-0.75, 0.50, 0.0, -0.75, 0.0],
                [0.75, -0.50, 0.0, -0.75, 0.0],
                [-0.75, -0.50, 0.0, -0.75, 0.0],
                [0.50, 0.75, -0.0, 0.75, -0.0],
                [-0.50, 0.75, -0.0, 0.75, -0.0],
                [0.50, -0.75, -0.0, 0.75, -0.0],
                [-0.50, -0.75, -0.0, 0.75, -0.0],
                [0.50, 0.75, 0.0, -0.75, -0.0],
                [-0.50, 0.75, 0.0, -0.75, -0.0],
                [0.50, -0.75, 0.0, -0.75, -0.0],
                [-0.50, -0.75, 0.0, -0.75, -0.0],
                [0.75, -0.0, 0.50, 0.75, 0.0],
                [-0.75, -0.0, 0.50, 0.75, 0.0],
                [0.75, 0.0, -0.50, 0.75, 0.0],
                [-0.75, 0.0, -0.50, 0.75, 0.0],
                [0.75, -0.0, 0.50, -0.75, 0.0],
                [-0.75, -0.0, 0.50, -0.75, 0.0],
                [0.75, 0.0, -0.50, -0.75, 0.0],
                [-0.75, 0.0, -0.50, -0.75, 0.0],
                [-0.0, 0.75, 0.50, 0.75, -0.0],
                [0.0, -0.75, 0.50, 0.75, -0.0],
                [-0.0, 0.75, -0.50, 0.75, -0.0],
                [0.0, -0.75, -0.50, 0.75, -0.0],
                [-0.0, 0.75, 0.50, -0.75, -0.0],
                [0.0, -0.75, 0.50, -0.75, -0.0],
                [-0.0, 0.75, -0.50, -0.75, -0.0],
                [0.0, -0.75, -0.50, -0.75, -0.0],
                [0.50, -0.0, 0.75, 0.75, 0.0],
                [-0.50, -0.0, 0.75, 0.75, 0.0],
                [0.50, 0.0, -0.75, 0.75, 0.0],
                [-0.50, 0.0, -0.75, 0.75, 0.0],
                [0.50, -0.0, 0.75, -0.75, 0.0],
                [-0.50, -0.0, 0.75, -0.75, 0.0],
                [0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.0, 0.50, 0.75, 0.75, -0.0],
                [0.0, -0.50, 0.75, 0.75, -0.0],
                [-0.0, 0.50, -0.75, 0.75, -0.0],
                [0.0, -0.50, -0.75, 0.75, -0.0],
                [-0.0, 0.50, 0.75, -0.75, -0.0],
                [0.0, -0.50, 0.75, -0.75, -0.0],
                [-0.0, 0.50, -0.75, -0.75, -0.0],
                [0.0, -0.50, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.50],
                [-0.75, 0.75, 0.0, -0.0, 0.50],
                [0.75, -0.75, 0.0, -0.0, 0.50],
                [-0.75, -0.75, 0.0, -0.0, 0.50],
                [0.75, 0.75, -0.0, 0.0, -0.50],
                [-0.75, 0.75, -0.0, 0.0, -0.50],
                [0.75, -0.75, -0.0, 0.0, -0.50],
                [-0.75, -0.75, -0.0, 0.0, -0.50],
                [0.75, 0.0, 0.75, -0.0, 0.50],
                [-0.75, 0.0, 0.75, -0.0, 0.50],
                [0.75, -0.0, -0.75, -0.0, 0.50],
                [-0.75, -0.0, -0.75, -0.0, 0.50],
                [0.75, 0.0, 0.75, 0.0, -0.50],
                [-0.75, 0.0, 0.75, 0.0, -0.50],
                [0.75, -0.0, -0.75, 0.0, -0.50],
                [-0.75, -0.0, -0.75, 0.0, -0.50],
                [0.0, 0.75, 0.75, -0.0, 0.50],
                [-0.0, -0.75, 0.75, -0.0, 0.50],
                [0.0, 0.75, -0.75, -0.0, 0.50],
                [-0.0, -0.75, -0.75, -0.0, 0.50],
                [0.0, 0.75, 0.75, 0.0, -0.50],
                [-0.0, -0.75, 0.75, 0.0, -0.50],
                [0.0, 0.75, -0.75, 0.0, -0.50],
                [-0.0, -0.75, -0.75, 0.0, -0.50],
                [0.75, -0.0, 0.0, 0.75, 0.50],
                [-0.75, -0.0, 0.0, 0.75, 0.50],
                [0.75, 0.0, -0.0, -0.75, 0.50],
                [-0.75, 0.0, -0.0, -0.75, 0.50],
                [0.75, -0.0, 0.0, 0.75, -0.50],
                [-0.75, -0.0, 0.0, 0.75, -0.50],
                [0.75, 0.0, -0.0, -0.75, -0.50],
                [-0.75, 0.0, -0.0, -0.75, -0.50],
                [-0.0, 0.75, 0.0, 0.75, 0.50],
                [0.0, -0.75, 0.0, 0.75, 0.50],
                [-0.0, 0.75, -0.0, -0.75, 0.50],
                [0.0, -0.75, -0.0, -0.75, 0.50],
                [-0.0, 0.75, 0.0, 0.75, -0.50],
                [0.0, -0.75, 0.0, 0.75, -0.50],
                [-0.0, 0.75, -0.0, -0.75, -0.50],
                [0.0, -0.75, -0.0, -0.75, -0.50],
                [0.0, -0.0, 0.75, 0.75, 0.50],
                [-0.0, 0.0, -0.75, 0.75, 0.50],
                [0.0, -0.0, 0.75, -0.75, 0.50],
                [-0.0, 0.0, -0.75, -0.75, 0.50],
                [0.0, -0.0, 0.75, 0.75, -0.50],
                [-0.0, 0.0, -0.75, 0.75, -0.50],
                [0.0, -0.0, 0.75, -0.75, -0.50],
                [-0.0, 0.0, -0.75, -0.75, -0.50],
                [0.75, 0.50, -0.0, 0.0, 0.75],
                [-0.75, 0.50, -0.0, 0.0, 0.75],
                [0.75, -0.50, -0.0, 0.0, 0.75],
                [-0.75, -0.50, -0.0, 0.0, 0.75],
                [0.75, 0.50, 0.0, -0.0, -0.75],
                [-0.75, 0.50, 0.0, -0.0, -0.75],
                [0.75, -0.50, 0.0, -0.0, -0.75],
                [-0.75, -0.50, 0.0, -0.0, -0.75],
                [0.50, 0.75, -0.0, 0.0, 0.75],
                [-0.50, 0.75, -0.0, 0.0, 0.75],
                [0.50, -0.75, -0.0, 0.0, 0.75],
                [-0.50, -0.75, -0.0, 0.0, 0.75],
                [0.50, 0.75, 0.0, -0.0, -0.75],
                [-0.50, 0.75, 0.0, -0.0, -0.75],
                [0.50, -0.75, 0.0, -0.0, -0.75],
                [-0.50, -0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, 0.50, 0.0, 0.75],
                [-0.75, -0.0, 0.50, 0.0, 0.75],
                [0.75, 0.0, -0.50, 0.0, 0.75],
                [-0.75, 0.0, -0.50, 0.0, 0.75],
                [0.75, -0.0, 0.50, -0.0, -0.75],
                [-0.75, -0.0, 0.50, -0.0, -0.75],
                [0.75, 0.0, -0.50, -0.0, -0.75],
                [-0.75, 0.0, -0.50, -0.0, -0.75],
                [-0.0, 0.75, 0.50, 0.0, 0.75],
                [0.0, -0.75, 0.50, 0.0, 0.75],
                [-0.0, 0.75, -0.50, 0.0, 0.75],
                [0.0, -0.75, -0.50, 0.0, 0.75],
                [-0.0, 0.75, 0.50, -0.0, -0.75],
                [0.0, -0.75, 0.50, -0.0, -0.75],
                [-0.0, 0.75, -0.50, -0.0, -0.75],
                [0.0, -0.75, -0.50, -0.0, -0.75],
                [0.50, -0.0, 0.75, 0.0, 0.75],
                [-0.50, -0.0, 0.75, 0.0, 0.75],
                [0.50, 0.0, -0.75, 0.0, 0.75],
                [-0.50, 0.0, -0.75, 0.0, 0.75],
                [0.50, -0.0, 0.75, -0.0, -0.75],
                [-0.50, -0.0, 0.75, -0.0, -0.75],
                [0.50, 0.0, -0.75, -0.0, -0.75],
                [-0.50, 0.0, -0.75, -0.0, -0.75],
                [-0.0, 0.50, 0.75, 0.0, 0.75],
                [0.0, -0.50, 0.75, 0.0, 0.75],
                [-0.0, 0.50, -0.75, 0.0, 0.75],
                [0.0, -0.50, -0.75, 0.0, 0.75],
                [-0.0, 0.50, 0.75, -0.0, -0.75],
                [0.0, -0.50, 0.75, -0.0, -0.75],
                [-0.0, 0.50, -0.75, -0.0, -0.75],
                [0.0, -0.50, -0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, 0.50, 0.75],
                [-0.75, 0.0, -0.0, 0.50, 0.75],
                [0.75, -0.0, 0.0, -0.50, 0.75],
                [-0.75, -0.0, 0.0, -0.50, 0.75],
                [0.75, 0.0, -0.0, 0.50, -0.75],
                [-0.75, 0.0, -0.0, 0.50, -0.75],
                [0.75, -0.0, 0.0, -0.50, -0.75],
                [-0.75, -0.0, 0.0, -0.50, -0.75],
                [0.0, 0.75, -0.0, 0.50, 0.75],
                [-0.0, -0.75, -0.0, 0.50, 0.75],
                [0.0, 0.75, 0.0, -0.50, 0.75],
                [-0.0, -0.75, 0.0, -0.50, 0.75],
                [0.0, 0.75, -0.0, 0.50, -0.75],
                [-0.0, -0.75, -0.0, 0.50, -0.75],
                [0.0, 0.75, 0.0, -0.50, -0.75],
                [-0.0, -0.75, 0.0, -0.50, -0.75],
                [-0.0, 0.0, 0.75, 0.50, 0.75],
                [0.0, -0.0, -0.75, 0.50, 0.75],
                [-0.0, 0.0, 0.75, -0.50, 0.75],
                [0.0, -0.0, -0.75, -0.50, 0.75],
                [-0.0, 0.0, 0.75, 0.50, -0.75],
                [0.0, -0.0, -0.75, 0.50, -0.75],
                [-0.0, 0.0, 0.75, -0.50, -0.75],
                [0.0, -0.0, -0.75, -0.50, -0.75],
                [0.50, 0.0, -0.0, 0.75, 0.75],
                [-0.50, 0.0, -0.0, 0.75, 0.75],
                [0.50, -0.0, 0.0, -0.75, 0.75],
                [-0.50, -0.0, 0.0, -0.75, 0.75],
                [0.50, 0.0, -0.0, 0.75, -0.75],
                [-0.50, 0.0, -0.0, 0.75, -0.75],
                [0.50, -0.0, 0.0, -0.75, -0.75],
                [-0.50, -0.0, 0.0, -0.75, -0.75],
                [0.0, 0.50, -0.0, 0.75, 0.75],
                [-0.0, -0.50, -0.0, 0.75, 0.75],
                [0.0, 0.50, 0.0, -0.75, 0.75],
                [-0.0, -0.50, 0.0, -0.75, 0.75],
                [0.0, 0.50, -0.0, 0.75, -0.75],
                [-0.0, -0.50, -0.0, 0.75, -0.75],
                [0.0, 0.50, 0.0, -0.75, -0.75],
                [-0.0, -0.50, 0.0, -0.75, -0.75],
                [-0.0, 0.0, 0.50, 0.75, 0.75],
                [0.0, -0.0, -0.50, 0.75, 0.75],
                [-0.0, 0.0, 0.50, -0.75, 0.75],
                [0.0, -0.0, -0.50, -0.75, 0.75],
                [-0.0, 0.0, 0.50, 0.75, -0.75],
                [0.0, -0.0, -0.50, 0.75, -0.75],
                [-0.0, 0.0, 0.50, -0.75, -0.75],
                [0.0, -0.0, -0.50, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.50, 0.0, 0.0, 0.0],
                [0.75, -0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.50, 0.0, 0.0, 0.0],
                [0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.50, 0.75, -0.0, -0.0, -0.0],
                [0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.50, -0.75, -0.0, -0.0, -0.0],
                [0.75, 0.0, 0.50, 0.0, 0.0],
                [-0.75, 0.0, 0.50, 0.0, 0.0],
                [0.75, -0.0, -0.50, 0.0, 0.0],
                [-0.75, -0.0, -0.50, 0.0, 0.0],
                [0.0, 0.75, 0.50, -0.0, -0.0],
                [-0.0, -0.75, 0.50, -0.0, -0.0],
                [0.0, 0.75, -0.50, -0.0, -0.0],
                [-0.0, -0.75, -0.50, -0.0, -0.0],
                [0.50, 0.0, 0.75, 0.0, 0.0],
                [-0.50, 0.0, 0.75, 0.0, 0.0],
                [0.50, -0.0, -0.75, 0.0, 0.0],
                [-0.50, -0.0, -0.75, 0.0, 0.0],
                [0.0, 0.50, 0.75, -0.0, -0.0],
                [-0.0, -0.50, 0.75, -0.0, -0.0],
                [0.0, 0.50, -0.75, -0.0, -0.0],
                [-0.0, -0.50, -0.75, -0.0, -0.0],
                [0.75, 0.0, 0.0, 0.50, 0.0],
                [-0.75, 0.0, 0.0, 0.50, 0.0],
                [0.75, -0.0, -0.0, -0.50, 0.0],
                [-0.75, -0.0, -0.0, -0.50, 0.0],
                [0.0, 0.75, 0.0, 0.50, -0.0],
                [-0.0, -0.75, 0.0, 0.50, -0.0],
                [0.0, 0.75, -0.0, -0.50, -0.0],
                [-0.0, -0.75, -0.0, -0.50, -0.0],
                [0.0, 0.0, 0.75, 0.50, 0.0],
                [-0.0, -0.0, -0.75, 0.50, 0.0],
                [0.0, 0.0, 0.75, -0.50, 0.0],
                [-0.0, -0.0, -0.75, -0.50, 0.0],
                [0.50, 0.0, 0.0, 0.75, -0.0],
                [-0.50, 0.0, 0.0, 0.75, -0.0],
                [0.50, -0.0, -0.0, -0.75, -0.0],
                [-0.50, -0.0, -0.0, -0.75, -0.0],
                [0.0, 0.50, 0.0, 0.75, 0.0],
                [-0.0, -0.50, 0.0, 0.75, 0.0],
                [0.0, 0.50, -0.0, -0.75, 0.0],
                [-0.0, -0.50, -0.0, -0.75, 0.0],
                [0.0, 0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.0, -0.50, 0.75, -0.0],
                [0.0, 0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.0, -0.50, -0.75, -0.0],
                [0.75, 0.0, 0.0, 0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.0, 0.50],
                [0.75, -0.0, -0.0, -0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.0, -0.50],
                [0.0, 0.75, 0.0, 0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.0, 0.50],
                [0.0, 0.75, -0.0, -0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.0, -0.50],
                [0.0, 0.0, 0.75, 0.0, 0.50],
                [-0.0, -0.0, -0.75, 0.0, 0.50],
                [0.0, 0.0, 0.75, -0.0, -0.50],
                [-0.0, -0.0, -0.75, -0.0, -0.50],
                [0.0, 0.0, 0.0, 0.75, 0.50],
                [-0.0, -0.0, -0.0, -0.75, 0.50],
                [0.0, 0.0, 0.0, 0.75, -0.50],
                [-0.0, -0.0, -0.0, -0.75, -0.50],
                [0.50, 0.0, 0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.0, 0.0, 0.75],
                [0.50, -0.0, -0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.0, -0.0, -0.75],
                [0.0, 0.50, 0.0, 0.0, 0.75],
                [-0.0, -0.50, 0.0, 0.0, 0.75],
                [0.0, 0.50, -0.0, -0.0, -0.75],
                [-0.0, -0.50, -0.0, -0.0, -0.75],
                [0.0, 0.0, 0.50, 0.0, 0.75],
                [-0.0, -0.0, -0.50, 0.0, 0.75],
                [0.0, 0.0, 0.50, -0.0, -0.75],
                [-0.0, -0.0, -0.50, -0.0, -0.75],
                [0.0, 0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.0, -0.0, -0.50, 0.75],
                [0.0, 0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.0, -0.0, -0.50, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.75, -0.0, 0.75, -0.0, -0.0],
                [0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.0, 0.75, 0.75, 0.0, 0.0],
                [0.0, -0.75, 0.75, 0.0, 0.0],
                [-0.0, 0.75, -0.75, 0.0, 0.0],
                [0.0, -0.75, -0.75, 0.0, 0.0],
                [0.75, -0.0, -0.0, 0.75, -0.0],
                [-0.75, -0.0, -0.0, 0.75, -0.0],
                [0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.0, 0.75, -0.0, 0.75, 0.0],
                [0.0, -0.75, -0.0, 0.75, 0.0],
                [-0.0, 0.75, 0.0, -0.75, 0.0],
                [0.0, -0.75, 0.0, -0.75, 0.0],
                [-0.0, -0.0, 0.75, 0.75, -0.0],
                [0.0, 0.0, -0.75, 0.75, -0.0],
                [-0.0, -0.0, 0.75, -0.75, -0.0],
                [0.0, 0.0, -0.75, -0.75, -0.0],
                [0.75, 0.0, -0.0, -0.0, 0.75],
                [-0.75, 0.0, -0.0, -0.0, 0.75],
                [0.75, -0.0, 0.0, 0.0, -0.75],
                [-0.75, -0.0, 0.0, 0.0, -0.75],
                [0.0, 0.75, -0.0, -0.0, 0.75],
                [-0.0, -0.75, -0.0, -0.0, 0.75],
                [0.0, 0.75, 0.0, 0.0, -0.75],
                [-0.0, -0.75, 0.0, 0.0, -0.75],
                [-0.0, 0.0, 0.75, -0.0, 0.75],
                [0.0, -0.0, -0.75, -0.0, 0.75],
                [-0.0, 0.0, 0.75, 0.0, -0.75],
                [0.0, -0.0, -0.75, 0.0, -0.75],
                [-0.0, 0.0, -0.0, 0.75, 0.75],
                [0.0, -0.0, 0.0, -0.75, 0.75],
                [-0.0, 0.0, -0.0, 0.75, -0.75],
                [0.0, -0.0, 0.0, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.0, -0.0, -0.0],
                [0.0, -0.75, -0.0, -0.0, -0.0],
                [0.0, -0.0, 0.75, 0.0, 0.0],
                [-0.0, 0.0, -0.75, 0.0, 0.0],
                [-0.0, -0.0, 0.0, 0.75, -0.0],
                [0.0, 0.0, -0.0, -0.75, -0.0],
                [0.0, 0.0, -0.0, -0.0, 0.75],
                [-0.0, -0.0, 0.0, 0.0, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim);
        }
    }

    #[test]
    fn check_ndim_6_generators() {
        let ndim = 6;

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.75, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75, 0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75, 0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, -0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, -0.75, 0.75, 0.75],
                [-0.75, 0.75, -0.75, -0.75, 0.75, 0.75],
                [0.75, -0.75, -0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, -0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, 0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75, -0.75, 0.75],
                [-0.75, 0.75, 0.75, -0.75, -0.75, 0.75],
                [0.75, -0.75, 0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75, -0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, -0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, 0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, 0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75, 0.75, 0.75, -0.75],
                [-0.75, -0.75, -0.75, 0.75, 0.75, -0.75],
                [0.75, 0.75, 0.75, -0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, 0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, 0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, 0.75, 0.75, -0.75, -0.75],
                [-0.75, -0.75, 0.75, 0.75, -0.75, -0.75],
                [0.75, 0.75, -0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, 0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, 0.75, -0.75, -0.75],
                [0.75, 0.75, 0.75, -0.75, -0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75, -0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75, -0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2usize.pow(ndim));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, -0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.75, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.75, 0.75, -0.0, 0.75, -0.0, -0.0],
                [0.75, -0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.75, -0.75, -0.0, 0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.75, 0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.75, -0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.0, 0.75, 0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.75, 0.75, 0.0, 0.0],
                [0.75, 0.0, -0.75, 0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.75, 0.75, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.75, -0.75, 0.0, 0.0],
                [0.75, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.75, 0.75, -0.0, -0.0],
                [0.0, -0.75, 0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.75, 0.75, -0.0, -0.0],
                [0.0, -0.75, -0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.75, 0.75, -0.75, -0.0, -0.0],
                [0.0, -0.75, 0.75, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.75, -0.75, -0.0, -0.0],
                [0.0, -0.75, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.75, 0.0],
                [-0.75, 0.75, 0.0, -0.0, 0.75, 0.0],
                [0.75, -0.75, 0.0, -0.0, 0.75, 0.0],
                [-0.75, -0.75, 0.0, -0.0, 0.75, 0.0],
                [0.75, 0.75, -0.0, 0.0, -0.75, 0.0],
                [-0.75, 0.75, -0.0, 0.0, -0.75, 0.0],
                [0.75, -0.75, -0.0, 0.0, -0.75, 0.0],
                [-0.75, -0.75, -0.0, 0.0, -0.75, 0.0],
                [0.75, 0.0, 0.75, -0.0, 0.75, -0.0],
                [-0.75, 0.0, 0.75, -0.0, 0.75, -0.0],
                [0.75, -0.0, -0.75, -0.0, 0.75, -0.0],
                [-0.75, -0.0, -0.75, -0.0, 0.75, -0.0],
                [0.75, 0.0, 0.75, 0.0, -0.75, -0.0],
                [-0.75, 0.0, 0.75, 0.0, -0.75, -0.0],
                [0.75, -0.0, -0.75, 0.0, -0.75, -0.0],
                [-0.75, -0.0, -0.75, 0.0, -0.75, -0.0],
                [0.0, 0.75, 0.75, -0.0, 0.75, 0.0],
                [-0.0, -0.75, 0.75, -0.0, 0.75, 0.0],
                [0.0, 0.75, -0.75, -0.0, 0.75, 0.0],
                [-0.0, -0.75, -0.75, -0.0, 0.75, 0.0],
                [0.0, 0.75, 0.75, 0.0, -0.75, 0.0],
                [-0.0, -0.75, 0.75, 0.0, -0.75, 0.0],
                [0.0, 0.75, -0.75, 0.0, -0.75, 0.0],
                [-0.0, -0.75, -0.75, 0.0, -0.75, 0.0],
                [0.75, -0.0, 0.0, 0.75, 0.75, -0.0],
                [-0.75, -0.0, 0.0, 0.75, 0.75, -0.0],
                [0.75, 0.0, -0.0, -0.75, 0.75, -0.0],
                [-0.75, 0.0, -0.0, -0.75, 0.75, -0.0],
                [0.75, -0.0, 0.0, 0.75, -0.75, -0.0],
                [-0.75, -0.0, 0.0, 0.75, -0.75, -0.0],
                [0.75, 0.0, -0.0, -0.75, -0.75, -0.0],
                [-0.75, 0.0, -0.0, -0.75, -0.75, -0.0],
                [-0.0, 0.75, 0.0, 0.75, 0.75, 0.0],
                [0.0, -0.75, 0.0, 0.75, 0.75, 0.0],
                [-0.0, 0.75, -0.0, -0.75, 0.75, 0.0],
                [0.0, -0.75, -0.0, -0.75, 0.75, 0.0],
                [-0.0, 0.75, 0.0, 0.75, -0.75, 0.0],
                [0.0, -0.75, 0.0, 0.75, -0.75, 0.0],
                [-0.0, 0.75, -0.0, -0.75, -0.75, 0.0],
                [0.0, -0.75, -0.0, -0.75, -0.75, 0.0],
                [0.0, -0.0, 0.75, 0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.75, 0.75, 0.75, -0.0],
                [0.0, -0.0, 0.75, -0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.75, -0.75, 0.75, -0.0],
                [0.0, -0.0, 0.75, 0.75, -0.75, -0.0],
                [-0.0, 0.0, -0.75, 0.75, -0.75, -0.0],
                [0.0, -0.0, 0.75, -0.75, -0.75, -0.0],
                [-0.0, 0.0, -0.75, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.75, 0.75, 0.0, -0.0, 0.0, 0.75],
                [0.75, -0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.75, -0.75, 0.0, -0.0, 0.0, 0.75],
                [0.75, 0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.75, 0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, -0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.75, -0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, 0.0, 0.75, -0.0, 0.0, 0.75],
                [-0.75, 0.0, 0.75, -0.0, 0.0, 0.75],
                [0.75, -0.0, -0.75, -0.0, 0.0, 0.75],
                [-0.75, -0.0, -0.75, -0.0, 0.0, 0.75],
                [0.75, 0.0, 0.75, 0.0, -0.0, -0.75],
                [-0.75, 0.0, 0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, -0.75, 0.0, -0.0, -0.75],
                [-0.75, -0.0, -0.75, 0.0, -0.0, -0.75],
                [0.0, 0.75, 0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.75, 0.75, -0.0, 0.0, 0.75],
                [0.0, 0.75, -0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.75, -0.75, -0.0, 0.0, 0.75],
                [0.0, 0.75, 0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.75, 0.75, 0.0, -0.0, -0.75],
                [0.0, 0.75, -0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.75, -0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, 0.0, 0.75, 0.0, 0.75],
                [-0.75, -0.0, 0.0, 0.75, 0.0, 0.75],
                [0.75, 0.0, -0.0, -0.75, 0.0, 0.75],
                [-0.75, 0.0, -0.0, -0.75, 0.0, 0.75],
                [0.75, -0.0, 0.0, 0.75, -0.0, -0.75],
                [-0.75, -0.0, 0.0, 0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.75, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.0, 0.75, 0.0, 0.75, 0.0, 0.75],
                [0.0, -0.75, 0.0, 0.75, 0.0, 0.75],
                [-0.0, 0.75, -0.0, -0.75, 0.0, 0.75],
                [0.0, -0.75, -0.0, -0.75, 0.0, 0.75],
                [-0.0, 0.75, 0.0, 0.75, -0.0, -0.75],
                [0.0, -0.75, 0.0, 0.75, -0.0, -0.75],
                [-0.0, 0.75, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.75, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.0, 0.75, 0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.75, 0.75, 0.0, 0.75],
                [0.0, -0.0, 0.75, -0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.75, -0.75, 0.0, 0.75],
                [0.0, -0.0, 0.75, 0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.75, 0.75, -0.0, -0.75],
                [0.0, -0.0, 0.75, -0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.75, -0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, 0.0, 0.75, 0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.75, 0.75],
                [0.75, -0.0, 0.0, -0.0, -0.75, 0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.75, 0.75],
                [0.75, 0.0, -0.0, 0.0, 0.75, -0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.75, -0.75],
                [0.75, -0.0, 0.0, -0.0, -0.75, -0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.75, -0.75],
                [0.0, 0.75, -0.0, 0.0, 0.75, 0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.75, 0.75],
                [0.0, 0.75, 0.0, -0.0, -0.75, 0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.75, 0.75],
                [0.0, 0.75, -0.0, 0.0, 0.75, -0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.75, -0.75],
                [0.0, 0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.75, 0.75],
                [0.0, -0.0, -0.75, 0.0, 0.75, 0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.75, 0.75],
                [0.0, -0.0, -0.75, -0.0, -0.75, 0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.75, -0.75],
                [0.0, -0.0, -0.75, 0.0, 0.75, -0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.75, -0.75],
                [0.0, -0.0, -0.75, -0.0, -0.75, -0.75],
                [0.0, 0.0, -0.0, 0.75, 0.75, 0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.75, 0.75],
                [0.0, 0.0, -0.0, 0.75, -0.75, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.75, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.75, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.75, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.75, -0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2) / 3);
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5, 0.0, 0.0, 0.0]);

            let should_be = vec![
                [0.75, 0.75, 0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.50, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.50, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.75, -0.50, 0.0, 0.0, 0.0],
                [0.75, -0.75, -0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.75, -0.50, 0.0, 0.0, 0.0],
                [0.75, 0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.50, 0.75, -0.0, -0.0, -0.0],
                [0.75, -0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.50, 0.75, -0.0, -0.0, -0.0],
                [0.75, 0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.50, -0.75, -0.0, -0.0, -0.0],
                [0.75, -0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.50, -0.75, -0.0, -0.0, -0.0],
                [0.50, 0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.50, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.75, 0.75, 0.0, 0.0, 0.0],
                [0.50, 0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.50, -0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.50, -0.0, -0.0],
                [-0.75, 0.75, -0.0, 0.50, -0.0, -0.0],
                [0.75, -0.75, -0.0, 0.50, -0.0, -0.0],
                [-0.75, -0.75, -0.0, 0.50, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.50, -0.0, -0.0],
                [-0.75, 0.75, 0.0, -0.50, -0.0, -0.0],
                [0.75, -0.75, 0.0, -0.50, -0.0, -0.0],
                [-0.75, -0.75, 0.0, -0.50, -0.0, -0.0],
                [0.75, -0.0, 0.75, 0.50, 0.0, 0.0],
                [-0.75, -0.0, 0.75, 0.50, 0.0, 0.0],
                [0.75, 0.0, -0.75, 0.50, 0.0, 0.0],
                [-0.75, 0.0, -0.75, 0.50, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.50, 0.0, 0.0],
                [-0.75, -0.0, 0.75, -0.50, 0.0, 0.0],
                [0.75, 0.0, -0.75, -0.50, 0.0, 0.0],
                [-0.75, 0.0, -0.75, -0.50, 0.0, 0.0],
                [-0.0, 0.75, 0.75, 0.50, -0.0, -0.0],
                [0.0, -0.75, 0.75, 0.50, -0.0, -0.0],
                [-0.0, 0.75, -0.75, 0.50, -0.0, -0.0],
                [0.0, -0.75, -0.75, 0.50, -0.0, -0.0],
                [-0.0, 0.75, 0.75, -0.50, -0.0, -0.0],
                [0.0, -0.75, 0.75, -0.50, -0.0, -0.0],
                [-0.0, 0.75, -0.75, -0.50, -0.0, -0.0],
                [0.0, -0.75, -0.75, -0.50, -0.0, -0.0],
                [0.75, 0.50, -0.0, 0.75, 0.0, 0.0],
                [-0.75, 0.50, -0.0, 0.75, 0.0, 0.0],
                [0.75, -0.50, -0.0, 0.75, 0.0, 0.0],
                [-0.75, -0.50, -0.0, 0.75, 0.0, 0.0],
                [0.75, 0.50, 0.0, -0.75, 0.0, 0.0],
                [-0.75, 0.50, 0.0, -0.75, 0.0, 0.0],
                [0.75, -0.50, 0.0, -0.75, 0.0, 0.0],
                [-0.75, -0.50, 0.0, -0.75, 0.0, 0.0],
                [0.50, 0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.50, 0.75, -0.0, 0.75, -0.0, -0.0],
                [0.50, -0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.50, -0.75, -0.0, 0.75, -0.0, -0.0],
                [0.50, 0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.50, 0.75, 0.0, -0.75, -0.0, -0.0],
                [0.50, -0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.50, -0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.0, 0.50, 0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.50, 0.75, 0.0, 0.0],
                [0.75, 0.0, -0.50, 0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.50, 0.75, 0.0, 0.0],
                [0.75, -0.0, 0.50, -0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.50, -0.75, 0.0, 0.0],
                [0.75, 0.0, -0.50, -0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.50, -0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.50, 0.75, -0.0, -0.0],
                [0.0, -0.75, 0.50, 0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.50, 0.75, -0.0, -0.0],
                [0.0, -0.75, -0.50, 0.75, -0.0, -0.0],
                [-0.0, 0.75, 0.50, -0.75, -0.0, -0.0],
                [0.0, -0.75, 0.50, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.50, -0.75, -0.0, -0.0],
                [0.0, -0.75, -0.50, -0.75, -0.0, -0.0],
                [0.50, -0.0, 0.75, 0.75, 0.0, 0.0],
                [-0.50, -0.0, 0.75, 0.75, 0.0, 0.0],
                [0.50, 0.0, -0.75, 0.75, 0.0, 0.0],
                [-0.50, 0.0, -0.75, 0.75, 0.0, 0.0],
                [0.50, -0.0, 0.75, -0.75, 0.0, 0.0],
                [-0.50, -0.0, 0.75, -0.75, 0.0, 0.0],
                [0.50, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.50, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.0, 0.50, 0.75, 0.75, -0.0, -0.0],
                [0.0, -0.50, 0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.50, -0.75, 0.75, -0.0, -0.0],
                [0.0, -0.50, -0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.50, 0.75, -0.75, -0.0, -0.0],
                [0.0, -0.50, 0.75, -0.75, -0.0, -0.0],
                [-0.0, 0.50, -0.75, -0.75, -0.0, -0.0],
                [0.0, -0.50, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.50, 0.0],
                [-0.75, 0.75, 0.0, -0.0, 0.50, 0.0],
                [0.75, -0.75, 0.0, -0.0, 0.50, 0.0],
                [-0.75, -0.75, 0.0, -0.0, 0.50, 0.0],
                [0.75, 0.75, -0.0, 0.0, -0.50, 0.0],
                [-0.75, 0.75, -0.0, 0.0, -0.50, 0.0],
                [0.75, -0.75, -0.0, 0.0, -0.50, 0.0],
                [-0.75, -0.75, -0.0, 0.0, -0.50, 0.0],
                [0.75, 0.0, 0.75, -0.0, 0.50, -0.0],
                [-0.75, 0.0, 0.75, -0.0, 0.50, -0.0],
                [0.75, -0.0, -0.75, -0.0, 0.50, -0.0],
                [-0.75, -0.0, -0.75, -0.0, 0.50, -0.0],
                [0.75, 0.0, 0.75, 0.0, -0.50, -0.0],
                [-0.75, 0.0, 0.75, 0.0, -0.50, -0.0],
                [0.75, -0.0, -0.75, 0.0, -0.50, -0.0],
                [-0.75, -0.0, -0.75, 0.0, -0.50, -0.0],
                [0.0, 0.75, 0.75, -0.0, 0.50, 0.0],
                [-0.0, -0.75, 0.75, -0.0, 0.50, 0.0],
                [0.0, 0.75, -0.75, -0.0, 0.50, 0.0],
                [-0.0, -0.75, -0.75, -0.0, 0.50, 0.0],
                [0.0, 0.75, 0.75, 0.0, -0.50, 0.0],
                [-0.0, -0.75, 0.75, 0.0, -0.50, 0.0],
                [0.0, 0.75, -0.75, 0.0, -0.50, 0.0],
                [-0.0, -0.75, -0.75, 0.0, -0.50, 0.0],
                [0.75, -0.0, 0.0, 0.75, 0.50, -0.0],
                [-0.75, -0.0, 0.0, 0.75, 0.50, -0.0],
                [0.75, 0.0, -0.0, -0.75, 0.50, -0.0],
                [-0.75, 0.0, -0.0, -0.75, 0.50, -0.0],
                [0.75, -0.0, 0.0, 0.75, -0.50, -0.0],
                [-0.75, -0.0, 0.0, 0.75, -0.50, -0.0],
                [0.75, 0.0, -0.0, -0.75, -0.50, -0.0],
                [-0.75, 0.0, -0.0, -0.75, -0.50, -0.0],
                [-0.0, 0.75, 0.0, 0.75, 0.50, 0.0],
                [0.0, -0.75, 0.0, 0.75, 0.50, 0.0],
                [-0.0, 0.75, -0.0, -0.75, 0.50, 0.0],
                [0.0, -0.75, -0.0, -0.75, 0.50, 0.0],
                [-0.0, 0.75, 0.0, 0.75, -0.50, 0.0],
                [0.0, -0.75, 0.0, 0.75, -0.50, 0.0],
                [-0.0, 0.75, -0.0, -0.75, -0.50, 0.0],
                [0.0, -0.75, -0.0, -0.75, -0.50, 0.0],
                [0.0, -0.0, 0.75, 0.75, 0.50, -0.0],
                [-0.0, 0.0, -0.75, 0.75, 0.50, -0.0],
                [0.0, -0.0, 0.75, -0.75, 0.50, -0.0],
                [-0.0, 0.0, -0.75, -0.75, 0.50, -0.0],
                [0.0, -0.0, 0.75, 0.75, -0.50, -0.0],
                [-0.0, 0.0, -0.75, 0.75, -0.50, -0.0],
                [0.0, -0.0, 0.75, -0.75, -0.50, -0.0],
                [-0.0, 0.0, -0.75, -0.75, -0.50, -0.0],
                [0.75, 0.50, -0.0, 0.0, 0.75, 0.0],
                [-0.75, 0.50, -0.0, 0.0, 0.75, 0.0],
                [0.75, -0.50, -0.0, 0.0, 0.75, 0.0],
                [-0.75, -0.50, -0.0, 0.0, 0.75, 0.0],
                [0.75, 0.50, 0.0, -0.0, -0.75, 0.0],
                [-0.75, 0.50, 0.0, -0.0, -0.75, 0.0],
                [0.75, -0.50, 0.0, -0.0, -0.75, 0.0],
                [-0.75, -0.50, 0.0, -0.0, -0.75, 0.0],
                [0.50, 0.75, -0.0, 0.0, 0.75, -0.0],
                [-0.50, 0.75, -0.0, 0.0, 0.75, -0.0],
                [0.50, -0.75, -0.0, 0.0, 0.75, -0.0],
                [-0.50, -0.75, -0.0, 0.0, 0.75, -0.0],
                [0.50, 0.75, 0.0, -0.0, -0.75, -0.0],
                [-0.50, 0.75, 0.0, -0.0, -0.75, -0.0],
                [0.50, -0.75, 0.0, -0.0, -0.75, -0.0],
                [-0.50, -0.75, 0.0, -0.0, -0.75, -0.0],
                [0.75, -0.0, 0.50, 0.0, 0.75, 0.0],
                [-0.75, -0.0, 0.50, 0.0, 0.75, 0.0],
                [0.75, 0.0, -0.50, 0.0, 0.75, 0.0],
                [-0.75, 0.0, -0.50, 0.0, 0.75, 0.0],
                [0.75, -0.0, 0.50, -0.0, -0.75, 0.0],
                [-0.75, -0.0, 0.50, -0.0, -0.75, 0.0],
                [0.75, 0.0, -0.50, -0.0, -0.75, 0.0],
                [-0.75, 0.0, -0.50, -0.0, -0.75, 0.0],
                [-0.0, 0.75, 0.50, 0.0, 0.75, -0.0],
                [0.0, -0.75, 0.50, 0.0, 0.75, -0.0],
                [-0.0, 0.75, -0.50, 0.0, 0.75, -0.0],
                [0.0, -0.75, -0.50, 0.0, 0.75, -0.0],
                [-0.0, 0.75, 0.50, -0.0, -0.75, -0.0],
                [0.0, -0.75, 0.50, -0.0, -0.75, -0.0],
                [-0.0, 0.75, -0.50, -0.0, -0.75, -0.0],
                [0.0, -0.75, -0.50, -0.0, -0.75, -0.0],
                [0.50, -0.0, 0.75, 0.0, 0.75, 0.0],
                [-0.50, -0.0, 0.75, 0.0, 0.75, 0.0],
                [0.50, 0.0, -0.75, 0.0, 0.75, 0.0],
                [-0.50, 0.0, -0.75, 0.0, 0.75, 0.0],
                [0.50, -0.0, 0.75, -0.0, -0.75, 0.0],
                [-0.50, -0.0, 0.75, -0.0, -0.75, 0.0],
                [0.50, 0.0, -0.75, -0.0, -0.75, 0.0],
                [-0.50, 0.0, -0.75, -0.0, -0.75, 0.0],
                [-0.0, 0.50, 0.75, 0.0, 0.75, -0.0],
                [0.0, -0.50, 0.75, 0.0, 0.75, -0.0],
                [-0.0, 0.50, -0.75, 0.0, 0.75, -0.0],
                [0.0, -0.50, -0.75, 0.0, 0.75, -0.0],
                [-0.0, 0.50, 0.75, -0.0, -0.75, -0.0],
                [0.0, -0.50, 0.75, -0.0, -0.75, -0.0],
                [-0.0, 0.50, -0.75, -0.0, -0.75, -0.0],
                [0.0, -0.50, -0.75, -0.0, -0.75, -0.0],
                [0.75, 0.0, -0.0, 0.50, 0.75, 0.0],
                [-0.75, 0.0, -0.0, 0.50, 0.75, 0.0],
                [0.75, -0.0, 0.0, -0.50, 0.75, 0.0],
                [-0.75, -0.0, 0.0, -0.50, 0.75, 0.0],
                [0.75, 0.0, -0.0, 0.50, -0.75, 0.0],
                [-0.75, 0.0, -0.0, 0.50, -0.75, 0.0],
                [0.75, -0.0, 0.0, -0.50, -0.75, 0.0],
                [-0.75, -0.0, 0.0, -0.50, -0.75, 0.0],
                [0.0, 0.75, -0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.75, -0.0, 0.50, 0.75, -0.0],
                [0.0, 0.75, 0.0, -0.50, 0.75, -0.0],
                [-0.0, -0.75, 0.0, -0.50, 0.75, -0.0],
                [0.0, 0.75, -0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.75, -0.0, 0.50, -0.75, -0.0],
                [0.0, 0.75, 0.0, -0.50, -0.75, -0.0],
                [-0.0, -0.75, 0.0, -0.50, -0.75, -0.0],
                [-0.0, 0.0, 0.75, 0.50, 0.75, 0.0],
                [0.0, -0.0, -0.75, 0.50, 0.75, 0.0],
                [-0.0, 0.0, 0.75, -0.50, 0.75, 0.0],
                [0.0, -0.0, -0.75, -0.50, 0.75, 0.0],
                [-0.0, 0.0, 0.75, 0.50, -0.75, 0.0],
                [0.0, -0.0, -0.75, 0.50, -0.75, 0.0],
                [-0.0, 0.0, 0.75, -0.50, -0.75, 0.0],
                [0.0, -0.0, -0.75, -0.50, -0.75, 0.0],
                [0.50, 0.0, -0.0, 0.75, 0.75, -0.0],
                [-0.50, 0.0, -0.0, 0.75, 0.75, -0.0],
                [0.50, -0.0, 0.0, -0.75, 0.75, -0.0],
                [-0.50, -0.0, 0.0, -0.75, 0.75, -0.0],
                [0.50, 0.0, -0.0, 0.75, -0.75, -0.0],
                [-0.50, 0.0, -0.0, 0.75, -0.75, -0.0],
                [0.50, -0.0, 0.0, -0.75, -0.75, -0.0],
                [-0.50, -0.0, 0.0, -0.75, -0.75, -0.0],
                [0.0, 0.50, -0.0, 0.75, 0.75, 0.0],
                [-0.0, -0.50, -0.0, 0.75, 0.75, 0.0],
                [0.0, 0.50, 0.0, -0.75, 0.75, 0.0],
                [-0.0, -0.50, 0.0, -0.75, 0.75, 0.0],
                [0.0, 0.50, -0.0, 0.75, -0.75, 0.0],
                [-0.0, -0.50, -0.0, 0.75, -0.75, 0.0],
                [0.0, 0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.0, -0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.0, 0.0, 0.50, 0.75, 0.75, -0.0],
                [0.0, -0.0, -0.50, 0.75, 0.75, -0.0],
                [-0.0, 0.0, 0.50, -0.75, 0.75, -0.0],
                [0.0, -0.0, -0.50, -0.75, 0.75, -0.0],
                [-0.0, 0.0, 0.50, 0.75, -0.75, -0.0],
                [0.0, -0.0, -0.50, 0.75, -0.75, -0.0],
                [-0.0, 0.0, 0.50, -0.75, -0.75, -0.0],
                [0.0, -0.0, -0.50, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, 0.0, -0.0, 0.50],
                [-0.75, 0.75, 0.0, 0.0, -0.0, 0.50],
                [0.75, -0.75, 0.0, 0.0, -0.0, 0.50],
                [-0.75, -0.75, 0.0, 0.0, -0.0, 0.50],
                [0.75, 0.75, -0.0, -0.0, 0.0, -0.50],
                [-0.75, 0.75, -0.0, -0.0, 0.0, -0.50],
                [0.75, -0.75, -0.0, -0.0, 0.0, -0.50],
                [-0.75, -0.75, -0.0, -0.0, 0.0, -0.50],
                [0.75, 0.0, 0.75, 0.0, -0.0, 0.50],
                [-0.75, 0.0, 0.75, 0.0, -0.0, 0.50],
                [0.75, -0.0, -0.75, 0.0, -0.0, 0.50],
                [-0.75, -0.0, -0.75, 0.0, -0.0, 0.50],
                [0.75, 0.0, 0.75, -0.0, 0.0, -0.50],
                [-0.75, 0.0, 0.75, -0.0, 0.0, -0.50],
                [0.75, -0.0, -0.75, -0.0, 0.0, -0.50],
                [-0.75, -0.0, -0.75, -0.0, 0.0, -0.50],
                [0.0, 0.75, 0.75, 0.0, -0.0, 0.50],
                [-0.0, -0.75, 0.75, 0.0, -0.0, 0.50],
                [0.0, 0.75, -0.75, 0.0, -0.0, 0.50],
                [-0.0, -0.75, -0.75, 0.0, -0.0, 0.50],
                [0.0, 0.75, 0.75, -0.0, 0.0, -0.50],
                [-0.0, -0.75, 0.75, -0.0, 0.0, -0.50],
                [0.0, 0.75, -0.75, -0.0, 0.0, -0.50],
                [-0.0, -0.75, -0.75, -0.0, 0.0, -0.50],
                [0.75, 0.0, 0.0, 0.75, -0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.75, -0.0, 0.50],
                [0.75, -0.0, -0.0, -0.75, -0.0, 0.50],
                [-0.75, -0.0, -0.0, -0.75, -0.0, 0.50],
                [0.75, 0.0, 0.0, 0.75, 0.0, -0.50],
                [-0.75, 0.0, 0.0, 0.75, 0.0, -0.50],
                [0.75, -0.0, -0.0, -0.75, 0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.75, 0.0, -0.50],
                [0.0, 0.75, 0.0, 0.75, -0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.75, -0.0, 0.50],
                [0.0, 0.75, -0.0, -0.75, -0.0, 0.50],
                [-0.0, -0.75, -0.0, -0.75, -0.0, 0.50],
                [0.0, 0.75, 0.0, 0.75, 0.0, -0.50],
                [-0.0, -0.75, 0.0, 0.75, 0.0, -0.50],
                [0.0, 0.75, -0.0, -0.75, 0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.75, 0.0, -0.50],
                [0.0, 0.0, 0.75, 0.75, -0.0, 0.50],
                [-0.0, -0.0, -0.75, 0.75, -0.0, 0.50],
                [0.0, 0.0, 0.75, -0.75, -0.0, 0.50],
                [-0.0, -0.0, -0.75, -0.75, -0.0, 0.50],
                [0.0, 0.0, 0.75, 0.75, 0.0, -0.50],
                [-0.0, -0.0, -0.75, 0.75, 0.0, -0.50],
                [0.0, 0.0, 0.75, -0.75, 0.0, -0.50],
                [-0.0, -0.0, -0.75, -0.75, 0.0, -0.50],
                [0.75, -0.0, 0.0, 0.0, 0.75, 0.50],
                [-0.75, -0.0, 0.0, 0.0, 0.75, 0.50],
                [0.75, 0.0, -0.0, -0.0, -0.75, 0.50],
                [-0.75, 0.0, -0.0, -0.0, -0.75, 0.50],
                [0.75, -0.0, 0.0, 0.0, 0.75, -0.50],
                [-0.75, -0.0, 0.0, 0.0, 0.75, -0.50],
                [0.75, 0.0, -0.0, -0.0, -0.75, -0.50],
                [-0.75, 0.0, -0.0, -0.0, -0.75, -0.50],
                [-0.0, 0.75, 0.0, 0.0, 0.75, 0.50],
                [0.0, -0.75, 0.0, 0.0, 0.75, 0.50],
                [-0.0, 0.75, -0.0, -0.0, -0.75, 0.50],
                [0.0, -0.75, -0.0, -0.0, -0.75, 0.50],
                [-0.0, 0.75, 0.0, 0.0, 0.75, -0.50],
                [0.0, -0.75, 0.0, 0.0, 0.75, -0.50],
                [-0.0, 0.75, -0.0, -0.0, -0.75, -0.50],
                [0.0, -0.75, -0.0, -0.0, -0.75, -0.50],
                [0.0, -0.0, 0.75, 0.0, 0.75, 0.50],
                [-0.0, 0.0, -0.75, 0.0, 0.75, 0.50],
                [0.0, -0.0, 0.75, -0.0, -0.75, 0.50],
                [-0.0, 0.0, -0.75, -0.0, -0.75, 0.50],
                [0.0, -0.0, 0.75, 0.0, 0.75, -0.50],
                [-0.0, 0.0, -0.75, 0.0, 0.75, -0.50],
                [0.0, -0.0, 0.75, -0.0, -0.75, -0.50],
                [-0.0, 0.0, -0.75, -0.0, -0.75, -0.50],
                [0.0, -0.0, 0.0, 0.75, 0.75, 0.50],
                [-0.0, 0.0, -0.0, -0.75, 0.75, 0.50],
                [0.0, -0.0, 0.0, 0.75, -0.75, 0.50],
                [-0.0, 0.0, -0.0, -0.75, -0.75, 0.50],
                [0.0, -0.0, 0.0, 0.75, 0.75, -0.50],
                [-0.0, 0.0, -0.0, -0.75, 0.75, -0.50],
                [0.0, -0.0, 0.0, 0.75, -0.75, -0.50],
                [-0.0, 0.0, -0.0, -0.75, -0.75, -0.50],
                [0.75, 0.50, 0.0, -0.0, 0.0, 0.75],
                [-0.75, 0.50, 0.0, -0.0, 0.0, 0.75],
                [0.75, -0.50, 0.0, -0.0, 0.0, 0.75],
                [-0.75, -0.50, 0.0, -0.0, 0.0, 0.75],
                [0.75, 0.50, -0.0, 0.0, -0.0, -0.75],
                [-0.75, 0.50, -0.0, 0.0, -0.0, -0.75],
                [0.75, -0.50, -0.0, 0.0, -0.0, -0.75],
                [-0.75, -0.50, -0.0, 0.0, -0.0, -0.75],
                [0.50, 0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.50, 0.75, 0.0, -0.0, 0.0, 0.75],
                [0.50, -0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.50, -0.75, 0.0, -0.0, 0.0, 0.75],
                [0.50, 0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.50, 0.75, -0.0, 0.0, -0.0, -0.75],
                [0.50, -0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.50, -0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, 0.0, 0.50, -0.0, 0.0, 0.75],
                [-0.75, 0.0, 0.50, -0.0, 0.0, 0.75],
                [0.75, -0.0, -0.50, -0.0, 0.0, 0.75],
                [-0.75, -0.0, -0.50, -0.0, 0.0, 0.75],
                [0.75, 0.0, 0.50, 0.0, -0.0, -0.75],
                [-0.75, 0.0, 0.50, 0.0, -0.0, -0.75],
                [0.75, -0.0, -0.50, 0.0, -0.0, -0.75],
                [-0.75, -0.0, -0.50, 0.0, -0.0, -0.75],
                [0.0, 0.75, 0.50, -0.0, 0.0, 0.75],
                [-0.0, -0.75, 0.50, -0.0, 0.0, 0.75],
                [0.0, 0.75, -0.50, -0.0, 0.0, 0.75],
                [-0.0, -0.75, -0.50, -0.0, 0.0, 0.75],
                [0.0, 0.75, 0.50, 0.0, -0.0, -0.75],
                [-0.0, -0.75, 0.50, 0.0, -0.0, -0.75],
                [0.0, 0.75, -0.50, 0.0, -0.0, -0.75],
                [-0.0, -0.75, -0.50, 0.0, -0.0, -0.75],
                [0.50, 0.0, 0.75, -0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.75, -0.0, 0.0, 0.75],
                [0.50, -0.0, -0.75, -0.0, 0.0, 0.75],
                [-0.50, -0.0, -0.75, -0.0, 0.0, 0.75],
                [0.50, 0.0, 0.75, 0.0, -0.0, -0.75],
                [-0.50, 0.0, 0.75, 0.0, -0.0, -0.75],
                [0.50, -0.0, -0.75, 0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.75, 0.0, -0.0, -0.75],
                [0.0, 0.50, 0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.50, 0.75, -0.0, 0.0, 0.75],
                [0.0, 0.50, -0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.50, -0.75, -0.0, 0.0, 0.75],
                [0.0, 0.50, 0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.50, 0.75, 0.0, -0.0, -0.75],
                [0.0, 0.50, -0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.50, -0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, 0.0, 0.50, 0.0, 0.75],
                [-0.75, -0.0, 0.0, 0.50, 0.0, 0.75],
                [0.75, 0.0, -0.0, -0.50, 0.0, 0.75],
                [-0.75, 0.0, -0.0, -0.50, 0.0, 0.75],
                [0.75, -0.0, 0.0, 0.50, -0.0, -0.75],
                [-0.75, -0.0, 0.0, 0.50, -0.0, -0.75],
                [0.75, 0.0, -0.0, -0.50, -0.0, -0.75],
                [-0.75, 0.0, -0.0, -0.50, -0.0, -0.75],
                [-0.0, 0.75, 0.0, 0.50, 0.0, 0.75],
                [0.0, -0.75, 0.0, 0.50, 0.0, 0.75],
                [-0.0, 0.75, -0.0, -0.50, 0.0, 0.75],
                [0.0, -0.75, -0.0, -0.50, 0.0, 0.75],
                [-0.0, 0.75, 0.0, 0.50, -0.0, -0.75],
                [0.0, -0.75, 0.0, 0.50, -0.0, -0.75],
                [-0.0, 0.75, -0.0, -0.50, -0.0, -0.75],
                [0.0, -0.75, -0.0, -0.50, -0.0, -0.75],
                [0.0, -0.0, 0.75, 0.50, 0.0, 0.75],
                [-0.0, 0.0, -0.75, 0.50, 0.0, 0.75],
                [0.0, -0.0, 0.75, -0.50, 0.0, 0.75],
                [-0.0, 0.0, -0.75, -0.50, 0.0, 0.75],
                [0.0, -0.0, 0.75, 0.50, -0.0, -0.75],
                [-0.0, 0.0, -0.75, 0.50, -0.0, -0.75],
                [0.0, -0.0, 0.75, -0.50, -0.0, -0.75],
                [-0.0, 0.0, -0.75, -0.50, -0.0, -0.75],
                [0.50, -0.0, 0.0, 0.75, 0.0, 0.75],
                [-0.50, -0.0, 0.0, 0.75, 0.0, 0.75],
                [0.50, 0.0, -0.0, -0.75, 0.0, 0.75],
                [-0.50, 0.0, -0.0, -0.75, 0.0, 0.75],
                [0.50, -0.0, 0.0, 0.75, -0.0, -0.75],
                [-0.50, -0.0, 0.0, 0.75, -0.0, -0.75],
                [0.50, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.50, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.0, 0.50, 0.0, 0.75, 0.0, 0.75],
                [0.0, -0.50, 0.0, 0.75, 0.0, 0.75],
                [-0.0, 0.50, -0.0, -0.75, 0.0, 0.75],
                [0.0, -0.50, -0.0, -0.75, 0.0, 0.75],
                [-0.0, 0.50, 0.0, 0.75, -0.0, -0.75],
                [0.0, -0.50, 0.0, 0.75, -0.0, -0.75],
                [-0.0, 0.50, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.50, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.0, 0.50, 0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.50, 0.75, 0.0, 0.75],
                [0.0, -0.0, 0.50, -0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.50, -0.75, 0.0, 0.75],
                [0.0, -0.0, 0.50, 0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.50, 0.75, -0.0, -0.75],
                [0.0, -0.0, 0.50, -0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.50, -0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, 0.0, 0.50, 0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.50, 0.75],
                [0.75, -0.0, 0.0, -0.0, -0.50, 0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.50, 0.75],
                [0.75, 0.0, -0.0, 0.0, 0.50, -0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.50, -0.75],
                [0.75, -0.0, 0.0, -0.0, -0.50, -0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.50, -0.75],
                [0.0, 0.75, -0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.50, 0.75],
                [0.0, 0.75, 0.0, -0.0, -0.50, 0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.50, 0.75],
                [0.0, 0.75, -0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.50, -0.75],
                [0.0, 0.75, 0.0, -0.0, -0.50, -0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.50, -0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.50, 0.75],
                [0.0, -0.0, -0.75, 0.0, 0.50, 0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.50, 0.75],
                [0.0, -0.0, -0.75, -0.0, -0.50, 0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.50, -0.75],
                [0.0, -0.0, -0.75, 0.0, 0.50, -0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.50, -0.75],
                [0.0, -0.0, -0.75, -0.0, -0.50, -0.75],
                [0.0, 0.0, -0.0, 0.75, 0.50, 0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.50, 0.75],
                [0.0, 0.0, -0.0, 0.75, -0.50, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.50, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.50, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.50, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.50, -0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.50, -0.75],
                [0.50, -0.0, 0.0, 0.0, 0.75, 0.75],
                [-0.50, -0.0, 0.0, 0.0, 0.75, 0.75],
                [0.50, 0.0, -0.0, -0.0, -0.75, 0.75],
                [-0.50, 0.0, -0.0, -0.0, -0.75, 0.75],
                [0.50, -0.0, 0.0, 0.0, 0.75, -0.75],
                [-0.50, -0.0, 0.0, 0.0, 0.75, -0.75],
                [0.50, 0.0, -0.0, -0.0, -0.75, -0.75],
                [-0.50, 0.0, -0.0, -0.0, -0.75, -0.75],
                [-0.0, 0.50, 0.0, 0.0, 0.75, 0.75],
                [0.0, -0.50, 0.0, 0.0, 0.75, 0.75],
                [-0.0, 0.50, -0.0, -0.0, -0.75, 0.75],
                [0.0, -0.50, -0.0, -0.0, -0.75, 0.75],
                [-0.0, 0.50, 0.0, 0.0, 0.75, -0.75],
                [0.0, -0.50, 0.0, 0.0, 0.75, -0.75],
                [-0.0, 0.50, -0.0, -0.0, -0.75, -0.75],
                [0.0, -0.50, -0.0, -0.0, -0.75, -0.75],
                [0.0, -0.0, 0.50, 0.0, 0.75, 0.75],
                [-0.0, 0.0, -0.50, 0.0, 0.75, 0.75],
                [0.0, -0.0, 0.50, -0.0, -0.75, 0.75],
                [-0.0, 0.0, -0.50, -0.0, -0.75, 0.75],
                [0.0, -0.0, 0.50, 0.0, 0.75, -0.75],
                [-0.0, 0.0, -0.50, 0.0, 0.75, -0.75],
                [0.0, -0.0, 0.50, -0.0, -0.75, -0.75],
                [-0.0, 0.0, -0.50, -0.0, -0.75, -0.75],
                [0.0, -0.0, 0.0, 0.50, 0.75, 0.75],
                [-0.0, 0.0, -0.0, -0.50, 0.75, 0.75],
                [0.0, -0.0, 0.0, 0.50, -0.75, 0.75],
                [-0.0, 0.0, -0.0, -0.50, -0.75, 0.75],
                [0.0, -0.0, 0.0, 0.50, 0.75, -0.75],
                [-0.0, 0.0, -0.0, -0.50, 0.75, -0.75],
                [0.0, -0.0, 0.0, 0.50, -0.75, -0.75],
                [-0.0, 0.0, -0.0, -0.50, -0.75, -0.75],
            ];
            let should_be = should_be.iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1) * (ndim - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.50, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.50, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.50, 0.0, 0.0, 0.0, 0.0],
                [-0.75, -0.50, 0.0, 0.0, 0.0, 0.0],
                [0.50, 0.75, -0.0, -0.0, -0.0, -0.0],
                [-0.50, 0.75, -0.0, -0.0, -0.0, -0.0],
                [0.50, -0.75, -0.0, -0.0, -0.0, -0.0],
                [-0.50, -0.75, -0.0, -0.0, -0.0, -0.0],
                [0.75, 0.0, 0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.50, 0.0, 0.0, 0.0],
                [0.75, -0.0, -0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.0, -0.50, 0.0, 0.0, 0.0],
                [0.0, 0.75, 0.50, -0.0, -0.0, -0.0],
                [-0.0, -0.75, 0.50, -0.0, -0.0, -0.0],
                [0.0, 0.75, -0.50, -0.0, -0.0, -0.0],
                [-0.0, -0.75, -0.50, -0.0, -0.0, -0.0],
                [0.50, 0.0, 0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.0, 0.75, 0.0, 0.0, 0.0],
                [0.50, -0.0, -0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.0, -0.75, 0.0, 0.0, 0.0],
                [0.0, 0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.0, -0.50, 0.75, -0.0, -0.0, -0.0],
                [0.0, 0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.0, -0.50, -0.75, -0.0, -0.0, -0.0],
                [0.75, 0.0, 0.0, 0.50, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.50, 0.0, 0.0],
                [0.75, -0.0, -0.0, -0.50, 0.0, 0.0],
                [-0.75, -0.0, -0.0, -0.50, 0.0, 0.0],
                [0.0, 0.75, 0.0, 0.50, -0.0, -0.0],
                [-0.0, -0.75, 0.0, 0.50, -0.0, -0.0],
                [0.0, 0.75, -0.0, -0.50, -0.0, -0.0],
                [-0.0, -0.75, -0.0, -0.50, -0.0, -0.0],
                [0.0, 0.0, 0.75, 0.50, 0.0, 0.0],
                [-0.0, -0.0, -0.75, 0.50, 0.0, 0.0],
                [0.0, 0.0, 0.75, -0.50, 0.0, 0.0],
                [-0.0, -0.0, -0.75, -0.50, 0.0, 0.0],
                [0.50, 0.0, 0.0, 0.75, -0.0, -0.0],
                [-0.50, 0.0, 0.0, 0.75, -0.0, -0.0],
                [0.50, -0.0, -0.0, -0.75, -0.0, -0.0],
                [-0.50, -0.0, -0.0, -0.75, -0.0, -0.0],
                [0.0, 0.50, 0.0, 0.75, 0.0, 0.0],
                [-0.0, -0.50, 0.0, 0.75, 0.0, 0.0],
                [0.0, 0.50, -0.0, -0.75, 0.0, 0.0],
                [-0.0, -0.50, -0.0, -0.75, 0.0, 0.0],
                [0.0, 0.0, 0.50, 0.75, -0.0, -0.0],
                [-0.0, -0.0, -0.50, 0.75, -0.0, -0.0],
                [0.0, 0.0, 0.50, -0.75, -0.0, -0.0],
                [-0.0, -0.0, -0.50, -0.75, -0.0, -0.0],
                [0.75, 0.0, 0.0, 0.0, 0.50, 0.0],
                [-0.75, 0.0, 0.0, 0.0, 0.50, 0.0],
                [0.75, -0.0, -0.0, -0.0, -0.50, 0.0],
                [-0.75, -0.0, -0.0, -0.0, -0.50, 0.0],
                [0.0, 0.75, 0.0, 0.0, 0.50, -0.0],
                [-0.0, -0.75, 0.0, 0.0, 0.50, -0.0],
                [0.0, 0.75, -0.0, -0.0, -0.50, -0.0],
                [-0.0, -0.75, -0.0, -0.0, -0.50, -0.0],
                [0.0, 0.0, 0.75, 0.0, 0.50, 0.0],
                [-0.0, -0.0, -0.75, 0.0, 0.50, 0.0],
                [0.0, 0.0, 0.75, -0.0, -0.50, 0.0],
                [-0.0, -0.0, -0.75, -0.0, -0.50, 0.0],
                [0.0, 0.0, 0.0, 0.75, 0.50, -0.0],
                [-0.0, -0.0, -0.0, -0.75, 0.50, -0.0],
                [0.0, 0.0, 0.0, 0.75, -0.50, -0.0],
                [-0.0, -0.0, -0.0, -0.75, -0.50, -0.0],
                [0.50, 0.0, 0.0, 0.0, 0.75, 0.0],
                [-0.50, 0.0, 0.0, 0.0, 0.75, 0.0],
                [0.50, -0.0, -0.0, -0.0, -0.75, 0.0],
                [-0.50, -0.0, -0.0, -0.0, -0.75, 0.0],
                [0.0, 0.50, 0.0, 0.0, 0.75, -0.0],
                [-0.0, -0.50, 0.0, 0.0, 0.75, -0.0],
                [0.0, 0.50, -0.0, -0.0, -0.75, -0.0],
                [-0.0, -0.50, -0.0, -0.0, -0.75, -0.0],
                [0.0, 0.0, 0.50, 0.0, 0.75, 0.0],
                [-0.0, -0.0, -0.50, 0.0, 0.75, 0.0],
                [0.0, 0.0, 0.50, -0.0, -0.75, 0.0],
                [-0.0, -0.0, -0.50, -0.0, -0.75, 0.0],
                [0.0, 0.0, 0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.0, -0.0, -0.50, 0.75, -0.0],
                [0.0, 0.0, 0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.0, -0.0, -0.50, -0.75, -0.0],
                [0.75, 0.0, 0.0, 0.0, 0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.0, 0.0, 0.50],
                [0.75, -0.0, -0.0, -0.0, -0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.0, -0.0, -0.50],
                [0.0, 0.75, 0.0, 0.0, 0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.0, 0.0, 0.50],
                [0.0, 0.75, -0.0, -0.0, -0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.0, -0.0, -0.50],
                [0.0, 0.0, 0.75, 0.0, 0.0, 0.50],
                [-0.0, -0.0, -0.75, 0.0, 0.0, 0.50],
                [0.0, 0.0, 0.75, -0.0, -0.0, -0.50],
                [-0.0, -0.0, -0.75, -0.0, -0.0, -0.50],
                [0.0, 0.0, 0.0, 0.75, 0.0, 0.50],
                [-0.0, -0.0, -0.0, -0.75, 0.0, 0.50],
                [0.0, 0.0, 0.0, 0.75, -0.0, -0.50],
                [-0.0, -0.0, -0.0, -0.75, -0.0, -0.50],
                [0.0, 0.0, 0.0, 0.0, 0.75, 0.50],
                [-0.0, -0.0, -0.0, -0.0, -0.75, 0.50],
                [0.0, 0.0, 0.0, 0.0, 0.75, -0.50],
                [-0.0, -0.0, -0.0, -0.0, -0.75, -0.50],
                [0.50, 0.0, 0.0, 0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.0, 0.0, 0.0, 0.75],
                [0.50, -0.0, -0.0, -0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.0, -0.0, -0.0, -0.75],
                [0.0, 0.50, 0.0, 0.0, 0.0, 0.75],
                [-0.0, -0.50, 0.0, 0.0, 0.0, 0.75],
                [0.0, 0.50, -0.0, -0.0, -0.0, -0.75],
                [-0.0, -0.50, -0.0, -0.0, -0.0, -0.75],
                [0.0, 0.0, 0.50, 0.0, 0.0, 0.75],
                [-0.0, -0.0, -0.50, 0.0, 0.0, 0.75],
                [0.0, 0.0, 0.50, -0.0, -0.0, -0.75],
                [-0.0, -0.0, -0.50, -0.0, -0.0, -0.75],
                [0.0, 0.0, 0.0, 0.50, 0.0, 0.75],
                [-0.0, -0.0, -0.0, -0.50, 0.0, 0.75],
                [0.0, 0.0, 0.0, 0.50, -0.0, -0.75],
                [-0.0, -0.0, -0.0, -0.50, -0.0, -0.75],
                [0.0, 0.0, 0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.0, -0.0, -0.0, -0.50, 0.75],
                [0.0, 0.0, 0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.0, -0.0, -0.0, -0.50, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.0, 0.75, -0.0, -0.0, -0.0],
                [0.75, 0.0, -0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.0, -0.75, -0.0, -0.0, -0.0],
                [-0.0, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.0, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.0, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, -0.0, -0.0, 0.75, -0.0, -0.0],
                [-0.75, -0.0, -0.0, 0.75, -0.0, -0.0],
                [0.75, 0.0, 0.0, -0.75, -0.0, -0.0],
                [-0.75, 0.0, 0.0, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.0, 0.75, 0.0, 0.0],
                [0.0, -0.75, -0.0, 0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.0, -0.75, 0.0, 0.0],
                [0.0, -0.75, 0.0, -0.75, 0.0, 0.0],
                [-0.0, -0.0, 0.75, 0.75, -0.0, -0.0],
                [0.0, 0.0, -0.75, 0.75, -0.0, -0.0],
                [-0.0, -0.0, 0.75, -0.75, -0.0, -0.0],
                [0.0, 0.0, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.0, -0.0, -0.0, 0.75, 0.0],
                [-0.75, 0.0, -0.0, -0.0, 0.75, 0.0],
                [0.75, -0.0, 0.0, 0.0, -0.75, 0.0],
                [-0.75, -0.0, 0.0, 0.0, -0.75, 0.0],
                [0.0, 0.75, -0.0, -0.0, 0.75, -0.0],
                [-0.0, -0.75, -0.0, -0.0, 0.75, -0.0],
                [0.0, 0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.0, -0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.0, 0.0, 0.75, -0.0, 0.75, 0.0],
                [0.0, -0.0, -0.75, -0.0, 0.75, 0.0],
                [-0.0, 0.0, 0.75, 0.0, -0.75, 0.0],
                [0.0, -0.0, -0.75, 0.0, -0.75, 0.0],
                [-0.0, 0.0, -0.0, 0.75, 0.75, -0.0],
                [0.0, -0.0, 0.0, -0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.0, 0.75, -0.75, -0.0],
                [0.0, -0.0, 0.0, -0.75, -0.75, -0.0],
                [0.75, 0.0, -0.0, 0.0, -0.0, 0.75],
                [-0.75, 0.0, -0.0, 0.0, -0.0, 0.75],
                [0.75, -0.0, 0.0, -0.0, 0.0, -0.75],
                [-0.75, -0.0, 0.0, -0.0, 0.0, -0.75],
                [0.0, 0.75, -0.0, 0.0, -0.0, 0.75],
                [-0.0, -0.75, -0.0, 0.0, -0.0, 0.75],
                [0.0, 0.75, 0.0, -0.0, 0.0, -0.75],
                [-0.0, -0.75, 0.0, -0.0, 0.0, -0.75],
                [-0.0, 0.0, 0.75, 0.0, -0.0, 0.75],
                [0.0, -0.0, -0.75, 0.0, -0.0, 0.75],
                [-0.0, 0.0, 0.75, -0.0, 0.0, -0.75],
                [0.0, -0.0, -0.75, -0.0, 0.0, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.0, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.0, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.0, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.0, -0.75],
                [-0.0, -0.0, 0.0, 0.0, 0.75, 0.75],
                [0.0, 0.0, -0.0, -0.0, -0.75, 0.75],
                [-0.0, -0.0, 0.0, 0.0, 0.75, -0.75],
                [0.0, 0.0, -0.0, -0.0, -0.75, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim * (ndim - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.0, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.0, -0.0, -0.0, -0.0],
                [0.0, -0.75, -0.0, -0.0, -0.0, -0.0],
                [0.0, -0.0, 0.75, 0.0, 0.0, 0.0],
                [-0.0, 0.0, -0.75, 0.0, 0.0, 0.0],
                [-0.0, -0.0, 0.0, 0.75, -0.0, -0.0],
                [0.0, 0.0, -0.0, -0.75, -0.0, -0.0],
                [0.0, 0.0, -0.0, -0.0, 0.75, 0.0],
                [-0.0, -0.0, 0.0, 0.0, -0.75, 0.0],
                [-0.0, -0.0, -0.0, 0.0, 0.0, 0.75],
                [0.0, 0.0, 0.0, -0.0, -0.0, -0.75],
            ]
            .iter();

            let mut count = 0;
            for (a, b) in vv.permutations().zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * ndim);
        }
    }
}

#[cfg(test)]
#[allow(clippy::too_many_lines)]
mod tests_with_centre_and_half_widths {
    use super::*;
    use crate::multi::two_pow_n;

    const CV: f64 = 1.44e-4;
    const HWV: f64 = 2.2e-4;

    #[test]
    fn with_centre_hw_check_ndim_2_generators() {
        const N: usize = 2;

        let centre = [CV; N];
        let half_widths = [HWV; N];

        {
            let vv = Generator::new([0.75f64, 0.75]);

            let should_be = [[0.75, 0.75], [-0.75, 0.75], [0.75, -0.75], [-0.75, -0.75]]
                .map(|[a, b]| [CV + a * HWV, CV + b * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, two_pow_n(N));
        }

        {
            let vv = Generator::new([0.75f64, 0.5]);

            let should_be = [
                [0.75, 0.5],
                [-0.75, 0.5],
                [0.75, -0.5],
                [-0.75, -0.5],
                [0.5, 0.75],
                [-0.5, 0.75],
                [0.5, -0.75],
                [-0.5, -0.75],
            ]
            .map(|[a, b]| [CV + a * HWV, CV + b * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0]);

            let should_be = [
                [0.75f64, 0.0],
                [-0.75f64, 0.0],
                [0.0, 0.75f64],
                [0.0, -0.75f64],
            ]
            .map(|[a, b]| [CV + a * HWV, CV + b * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * N);
        }
    }

    #[test]
    fn with_centre_hw_check_ndim_3_generators() {
        const N: usize = 3;

        let centre = [CV; N];
        let half_widths = [HWV; N];

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75],
                [0.75, 0.75, 0.75],
            ]
            .map(|[a, b, c]| [CV + a * HWV, CV + b * HWV, CV + c * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, two_pow_n(N));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5]);

            let should_be = [
                [0.75, 0.75, 0.5],
                [-0.75, 0.75, 0.5],
                [0.75, -0.75, 0.5],
                [-0.75, -0.75, 0.5],
                [0.75, 0.75, -0.5],
                [-0.75, 0.75, -0.5],
                [0.75, -0.75, -0.5],
                [-0.75, -0.75, -0.5],
                [0.75, 0.5, 0.75],
                [-0.75, 0.5, 0.75],
                [0.75, -0.5, 0.75],
                [-0.75, -0.5, 0.75],
                [0.75, 0.5, -0.75],
                [-0.75, 0.5, -0.75],
                [0.75, -0.5, -0.75],
                [-0.75, -0.5, -0.75],
                [0.5, 0.75, 0.75],
                [-0.5, 0.75, 0.75],
                [0.5, -0.75, 0.75],
                [-0.5, -0.75, 0.75],
                [0.5, 0.75, -0.75],
                [-0.5, 0.75, -0.75],
                [0.5, -0.75, -0.75],
                [-0.5, -0.75, -0.75],
                [0.75, 0.75, 0.5],
            ]
            .map(|[a, b, c]| [CV + a * HWV, CV + b * HWV, CV + c * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1) * (N - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0]);

            let should_be = [
                [0.75f64, 0.5, 0.0],
                [-0.75f64, 0.5, 0.0],
                [0.75f64, -0.5, 0.0],
                [-0.75f64, -0.5, 0.0],
                [0.5, 0.75f64, 0.0],
                [-0.5, 0.75f64, 0.0],
                [0.5, -0.75f64, 0.0],
                [-0.5, -0.75f64, 0.0],
                [0.75f64, 0.0, 0.5],
                [-0.75f64, 0.0, 0.5],
                [0.75f64, 0.0, -0.5],
                [-0.75f64, 0.0, -0.5],
                [0.0, 0.75f64, 0.5],
                [0.0, -0.75f64, 0.5],
                [0.0, 0.75f64, -0.5],
                [0.0, -0.75f64, -0.5],
                [0.5, 0.0, 0.75f64],
                [-0.5, 0.0, 0.75f64],
                [0.5, 0.0, -0.75f64],
                [-0.5, 0.0, -0.75f64],
                [0.0, 0.5, 0.75f64],
                [0.0, -0.5, 0.75f64],
                [0.0, 0.5, -0.75f64],
                [0.0, -0.5, -0.75f64],
            ]
            .map(|[a, b, c]| [CV + a * HWV, CV + b * HWV, CV + c * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0]);

            let should_be = [
                [0.75f64, 0.75, 0.0],
                [-0.75f64, 0.75, 0.0],
                [0.75f64, -0.75, 0.0],
                [-0.75f64, -0.75, 0.0],
                [0.75f64, 0.0, 0.75],
                [-0.75f64, 0.0, 0.75],
                [0.75f64, 0.0, -0.75],
                [-0.75f64, 0.0, -0.75],
                [0.0, 0.75f64, 0.75],
                [0.0, -0.75f64, 0.75],
                [0.0, 0.75f64, -0.75],
                [0.0, -0.75f64, -0.75],
            ]
            .map(|[a, b, c]| [CV + a * HWV, CV + b * HWV, CV + c * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * N * (N - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0]);

            let should_be = [
                [0.75f64, 0.0, 0.0],
                [-0.75f64, 0.0, 0.0],
                [0.0, 0.75f64, 0.0],
                [0.0, -0.75f64, 0.0],
                [0.0, 0.0, 0.75],
                [0.0, -0.0, -0.75],
            ]
            .map(|[a, b, c]| [CV + a * HWV, CV + b * HWV, CV + c * HWV]);

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                println!("{a:?}");
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * N);
        }
    }

    #[test]
    fn with_centre_hw_check_ndim_6_generators() {
        const N: usize = 6;

        let centre = [CV; N];
        let half_widths = [HWV; N];

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.75, 0.75, 0.75]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75, 0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75, 0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75, 0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75, 0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75, 0.75, 0.75],
                [-0.75, 0.75, 0.75, -0.75, 0.75, 0.75],
                [0.75, -0.75, 0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, 0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, -0.75, -0.75, 0.75, 0.75],
                [-0.75, 0.75, -0.75, -0.75, 0.75, 0.75],
                [0.75, -0.75, -0.75, -0.75, 0.75, 0.75],
                [-0.75, -0.75, -0.75, -0.75, 0.75, 0.75],
                [0.75, 0.75, 0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, 0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, 0.75, 0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75, 0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75, 0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, 0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, 0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, 0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, -0.75, -0.75, 0.75],
                [-0.75, 0.75, 0.75, -0.75, -0.75, 0.75],
                [0.75, -0.75, 0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, 0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, -0.75, -0.75, -0.75, 0.75],
                [-0.75, 0.75, -0.75, -0.75, -0.75, 0.75],
                [0.75, -0.75, -0.75, -0.75, -0.75, 0.75],
                [-0.75, -0.75, -0.75, -0.75, -0.75, 0.75],
                [0.75, 0.75, 0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, 0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, 0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, 0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75, 0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75, 0.75, 0.75, -0.75],
                [-0.75, -0.75, -0.75, 0.75, 0.75, -0.75],
                [0.75, 0.75, 0.75, -0.75, 0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75, 0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75, 0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75, 0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75, 0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75, 0.75, -0.75],
                [0.75, 0.75, 0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, 0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, 0.75, 0.75, -0.75, -0.75],
                [-0.75, -0.75, 0.75, 0.75, -0.75, -0.75],
                [0.75, 0.75, -0.75, 0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, 0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, 0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, 0.75, -0.75, -0.75],
                [0.75, 0.75, 0.75, -0.75, -0.75, -0.75],
                [-0.75, 0.75, 0.75, -0.75, -0.75, -0.75],
                [0.75, -0.75, 0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, 0.75, -0.75, -0.75, -0.75],
                [0.75, 0.75, -0.75, -0.75, -0.75, -0.75],
                [-0.75, 0.75, -0.75, -0.75, -0.75, -0.75],
                [0.75, -0.75, -0.75, -0.75, -0.75, -0.75],
                [-0.75, -0.75, -0.75, -0.75, -0.75, -0.75],
            ]
            .map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, two_pow_n(N));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.75, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.75, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, -0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.75, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.75, 0.75, -0.0, 0.75, -0.0, -0.0],
                [0.75, -0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.75, -0.75, -0.0, 0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.75, 0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.75, -0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.0, 0.75, 0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.75, 0.75, 0.0, 0.0],
                [0.75, 0.0, -0.75, 0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.75, 0.75, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.75, -0.75, 0.0, 0.0],
                [0.75, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.75, 0.75, -0.0, -0.0],
                [0.0, -0.75, 0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.75, 0.75, -0.0, -0.0],
                [0.0, -0.75, -0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.75, 0.75, -0.75, -0.0, -0.0],
                [0.0, -0.75, 0.75, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.75, -0.75, -0.0, -0.0],
                [0.0, -0.75, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.75, 0.0],
                [-0.75, 0.75, 0.0, -0.0, 0.75, 0.0],
                [0.75, -0.75, 0.0, -0.0, 0.75, 0.0],
                [-0.75, -0.75, 0.0, -0.0, 0.75, 0.0],
                [0.75, 0.75, -0.0, 0.0, -0.75, 0.0],
                [-0.75, 0.75, -0.0, 0.0, -0.75, 0.0],
                [0.75, -0.75, -0.0, 0.0, -0.75, 0.0],
                [-0.75, -0.75, -0.0, 0.0, -0.75, 0.0],
                [0.75, 0.0, 0.75, -0.0, 0.75, -0.0],
                [-0.75, 0.0, 0.75, -0.0, 0.75, -0.0],
                [0.75, -0.0, -0.75, -0.0, 0.75, -0.0],
                [-0.75, -0.0, -0.75, -0.0, 0.75, -0.0],
                [0.75, 0.0, 0.75, 0.0, -0.75, -0.0],
                [-0.75, 0.0, 0.75, 0.0, -0.75, -0.0],
                [0.75, -0.0, -0.75, 0.0, -0.75, -0.0],
                [-0.75, -0.0, -0.75, 0.0, -0.75, -0.0],
                [0.0, 0.75, 0.75, -0.0, 0.75, 0.0],
                [-0.0, -0.75, 0.75, -0.0, 0.75, 0.0],
                [0.0, 0.75, -0.75, -0.0, 0.75, 0.0],
                [-0.0, -0.75, -0.75, -0.0, 0.75, 0.0],
                [0.0, 0.75, 0.75, 0.0, -0.75, 0.0],
                [-0.0, -0.75, 0.75, 0.0, -0.75, 0.0],
                [0.0, 0.75, -0.75, 0.0, -0.75, 0.0],
                [-0.0, -0.75, -0.75, 0.0, -0.75, 0.0],
                [0.75, -0.0, 0.0, 0.75, 0.75, -0.0],
                [-0.75, -0.0, 0.0, 0.75, 0.75, -0.0],
                [0.75, 0.0, -0.0, -0.75, 0.75, -0.0],
                [-0.75, 0.0, -0.0, -0.75, 0.75, -0.0],
                [0.75, -0.0, 0.0, 0.75, -0.75, -0.0],
                [-0.75, -0.0, 0.0, 0.75, -0.75, -0.0],
                [0.75, 0.0, -0.0, -0.75, -0.75, -0.0],
                [-0.75, 0.0, -0.0, -0.75, -0.75, -0.0],
                [-0.0, 0.75, 0.0, 0.75, 0.75, 0.0],
                [0.0, -0.75, 0.0, 0.75, 0.75, 0.0],
                [-0.0, 0.75, -0.0, -0.75, 0.75, 0.0],
                [0.0, -0.75, -0.0, -0.75, 0.75, 0.0],
                [-0.0, 0.75, 0.0, 0.75, -0.75, 0.0],
                [0.0, -0.75, 0.0, 0.75, -0.75, 0.0],
                [-0.0, 0.75, -0.0, -0.75, -0.75, 0.0],
                [0.0, -0.75, -0.0, -0.75, -0.75, 0.0],
                [0.0, -0.0, 0.75, 0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.75, 0.75, 0.75, -0.0],
                [0.0, -0.0, 0.75, -0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.75, -0.75, 0.75, -0.0],
                [0.0, -0.0, 0.75, 0.75, -0.75, -0.0],
                [-0.0, 0.0, -0.75, 0.75, -0.75, -0.0],
                [0.0, -0.0, 0.75, -0.75, -0.75, -0.0],
                [-0.0, 0.0, -0.75, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.75, 0.75, 0.0, -0.0, 0.0, 0.75],
                [0.75, -0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.75, -0.75, 0.0, -0.0, 0.0, 0.75],
                [0.75, 0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.75, 0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, -0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.75, -0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, 0.0, 0.75, -0.0, 0.0, 0.75],
                [-0.75, 0.0, 0.75, -0.0, 0.0, 0.75],
                [0.75, -0.0, -0.75, -0.0, 0.0, 0.75],
                [-0.75, -0.0, -0.75, -0.0, 0.0, 0.75],
                [0.75, 0.0, 0.75, 0.0, -0.0, -0.75],
                [-0.75, 0.0, 0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, -0.75, 0.0, -0.0, -0.75],
                [-0.75, -0.0, -0.75, 0.0, -0.0, -0.75],
                [0.0, 0.75, 0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.75, 0.75, -0.0, 0.0, 0.75],
                [0.0, 0.75, -0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.75, -0.75, -0.0, 0.0, 0.75],
                [0.0, 0.75, 0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.75, 0.75, 0.0, -0.0, -0.75],
                [0.0, 0.75, -0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.75, -0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, 0.0, 0.75, 0.0, 0.75],
                [-0.75, -0.0, 0.0, 0.75, 0.0, 0.75],
                [0.75, 0.0, -0.0, -0.75, 0.0, 0.75],
                [-0.75, 0.0, -0.0, -0.75, 0.0, 0.75],
                [0.75, -0.0, 0.0, 0.75, -0.0, -0.75],
                [-0.75, -0.0, 0.0, 0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.75, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.0, 0.75, 0.0, 0.75, 0.0, 0.75],
                [0.0, -0.75, 0.0, 0.75, 0.0, 0.75],
                [-0.0, 0.75, -0.0, -0.75, 0.0, 0.75],
                [0.0, -0.75, -0.0, -0.75, 0.0, 0.75],
                [-0.0, 0.75, 0.0, 0.75, -0.0, -0.75],
                [0.0, -0.75, 0.0, 0.75, -0.0, -0.75],
                [-0.0, 0.75, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.75, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.0, 0.75, 0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.75, 0.75, 0.0, 0.75],
                [0.0, -0.0, 0.75, -0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.75, -0.75, 0.0, 0.75],
                [0.0, -0.0, 0.75, 0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.75, 0.75, -0.0, -0.75],
                [0.0, -0.0, 0.75, -0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.75, -0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, 0.0, 0.75, 0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.75, 0.75],
                [0.75, -0.0, 0.0, -0.0, -0.75, 0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.75, 0.75],
                [0.75, 0.0, -0.0, 0.0, 0.75, -0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.75, -0.75],
                [0.75, -0.0, 0.0, -0.0, -0.75, -0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.75, -0.75],
                [0.0, 0.75, -0.0, 0.0, 0.75, 0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.75, 0.75],
                [0.0, 0.75, 0.0, -0.0, -0.75, 0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.75, 0.75],
                [0.0, 0.75, -0.0, 0.0, 0.75, -0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.75, -0.75],
                [0.0, 0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.75, -0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.75, 0.75],
                [0.0, -0.0, -0.75, 0.0, 0.75, 0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.75, 0.75],
                [0.0, -0.0, -0.75, -0.0, -0.75, 0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.75, -0.75],
                [0.0, -0.0, -0.75, 0.0, 0.75, -0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.75, -0.75],
                [0.0, -0.0, -0.75, -0.0, -0.75, -0.75],
                [0.0, 0.0, -0.0, 0.75, 0.75, 0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.75, 0.75],
                [0.0, 0.0, -0.0, 0.75, -0.75, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.75, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.75, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.75, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.75, -0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.75, -0.75],
            ]
            .map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1) * (N - 2) / 3);
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.5, 0.0, 0.0, 0.0]);

            let should_be = vec![
                [0.75, 0.75, 0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.50, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.50, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.75, -0.50, 0.0, 0.0, 0.0],
                [0.75, -0.75, -0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.75, -0.50, 0.0, 0.0, 0.0],
                [0.75, 0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.50, 0.75, -0.0, -0.0, -0.0],
                [0.75, -0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.50, 0.75, -0.0, -0.0, -0.0],
                [0.75, 0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.50, -0.75, -0.0, -0.0, -0.0],
                [0.75, -0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.50, -0.75, -0.0, -0.0, -0.0],
                [0.50, 0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.50, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.75, 0.75, 0.0, 0.0, 0.0],
                [0.50, 0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.50, -0.75, -0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, 0.75, -0.0, 0.50, -0.0, -0.0],
                [-0.75, 0.75, -0.0, 0.50, -0.0, -0.0],
                [0.75, -0.75, -0.0, 0.50, -0.0, -0.0],
                [-0.75, -0.75, -0.0, 0.50, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.50, -0.0, -0.0],
                [-0.75, 0.75, 0.0, -0.50, -0.0, -0.0],
                [0.75, -0.75, 0.0, -0.50, -0.0, -0.0],
                [-0.75, -0.75, 0.0, -0.50, -0.0, -0.0],
                [0.75, -0.0, 0.75, 0.50, 0.0, 0.0],
                [-0.75, -0.0, 0.75, 0.50, 0.0, 0.0],
                [0.75, 0.0, -0.75, 0.50, 0.0, 0.0],
                [-0.75, 0.0, -0.75, 0.50, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.50, 0.0, 0.0],
                [-0.75, -0.0, 0.75, -0.50, 0.0, 0.0],
                [0.75, 0.0, -0.75, -0.50, 0.0, 0.0],
                [-0.75, 0.0, -0.75, -0.50, 0.0, 0.0],
                [-0.0, 0.75, 0.75, 0.50, -0.0, -0.0],
                [0.0, -0.75, 0.75, 0.50, -0.0, -0.0],
                [-0.0, 0.75, -0.75, 0.50, -0.0, -0.0],
                [0.0, -0.75, -0.75, 0.50, -0.0, -0.0],
                [-0.0, 0.75, 0.75, -0.50, -0.0, -0.0],
                [0.0, -0.75, 0.75, -0.50, -0.0, -0.0],
                [-0.0, 0.75, -0.75, -0.50, -0.0, -0.0],
                [0.0, -0.75, -0.75, -0.50, -0.0, -0.0],
                [0.75, 0.50, -0.0, 0.75, 0.0, 0.0],
                [-0.75, 0.50, -0.0, 0.75, 0.0, 0.0],
                [0.75, -0.50, -0.0, 0.75, 0.0, 0.0],
                [-0.75, -0.50, -0.0, 0.75, 0.0, 0.0],
                [0.75, 0.50, 0.0, -0.75, 0.0, 0.0],
                [-0.75, 0.50, 0.0, -0.75, 0.0, 0.0],
                [0.75, -0.50, 0.0, -0.75, 0.0, 0.0],
                [-0.75, -0.50, 0.0, -0.75, 0.0, 0.0],
                [0.50, 0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.50, 0.75, -0.0, 0.75, -0.0, -0.0],
                [0.50, -0.75, -0.0, 0.75, -0.0, -0.0],
                [-0.50, -0.75, -0.0, 0.75, -0.0, -0.0],
                [0.50, 0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.50, 0.75, 0.0, -0.75, -0.0, -0.0],
                [0.50, -0.75, 0.0, -0.75, -0.0, -0.0],
                [-0.50, -0.75, 0.0, -0.75, -0.0, -0.0],
                [0.75, -0.0, 0.50, 0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.50, 0.75, 0.0, 0.0],
                [0.75, 0.0, -0.50, 0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.50, 0.75, 0.0, 0.0],
                [0.75, -0.0, 0.50, -0.75, 0.0, 0.0],
                [-0.75, -0.0, 0.50, -0.75, 0.0, 0.0],
                [0.75, 0.0, -0.50, -0.75, 0.0, 0.0],
                [-0.75, 0.0, -0.50, -0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.50, 0.75, -0.0, -0.0],
                [0.0, -0.75, 0.50, 0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.50, 0.75, -0.0, -0.0],
                [0.0, -0.75, -0.50, 0.75, -0.0, -0.0],
                [-0.0, 0.75, 0.50, -0.75, -0.0, -0.0],
                [0.0, -0.75, 0.50, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.50, -0.75, -0.0, -0.0],
                [0.0, -0.75, -0.50, -0.75, -0.0, -0.0],
                [0.50, -0.0, 0.75, 0.75, 0.0, 0.0],
                [-0.50, -0.0, 0.75, 0.75, 0.0, 0.0],
                [0.50, 0.0, -0.75, 0.75, 0.0, 0.0],
                [-0.50, 0.0, -0.75, 0.75, 0.0, 0.0],
                [0.50, -0.0, 0.75, -0.75, 0.0, 0.0],
                [-0.50, -0.0, 0.75, -0.75, 0.0, 0.0],
                [0.50, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.50, 0.0, -0.75, -0.75, 0.0, 0.0],
                [-0.0, 0.50, 0.75, 0.75, -0.0, -0.0],
                [0.0, -0.50, 0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.50, -0.75, 0.75, -0.0, -0.0],
                [0.0, -0.50, -0.75, 0.75, -0.0, -0.0],
                [-0.0, 0.50, 0.75, -0.75, -0.0, -0.0],
                [0.0, -0.50, 0.75, -0.75, -0.0, -0.0],
                [-0.0, 0.50, -0.75, -0.75, -0.0, -0.0],
                [0.0, -0.50, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.75, 0.0, -0.0, 0.50, 0.0],
                [-0.75, 0.75, 0.0, -0.0, 0.50, 0.0],
                [0.75, -0.75, 0.0, -0.0, 0.50, 0.0],
                [-0.75, -0.75, 0.0, -0.0, 0.50, 0.0],
                [0.75, 0.75, -0.0, 0.0, -0.50, 0.0],
                [-0.75, 0.75, -0.0, 0.0, -0.50, 0.0],
                [0.75, -0.75, -0.0, 0.0, -0.50, 0.0],
                [-0.75, -0.75, -0.0, 0.0, -0.50, 0.0],
                [0.75, 0.0, 0.75, -0.0, 0.50, -0.0],
                [-0.75, 0.0, 0.75, -0.0, 0.50, -0.0],
                [0.75, -0.0, -0.75, -0.0, 0.50, -0.0],
                [-0.75, -0.0, -0.75, -0.0, 0.50, -0.0],
                [0.75, 0.0, 0.75, 0.0, -0.50, -0.0],
                [-0.75, 0.0, 0.75, 0.0, -0.50, -0.0],
                [0.75, -0.0, -0.75, 0.0, -0.50, -0.0],
                [-0.75, -0.0, -0.75, 0.0, -0.50, -0.0],
                [0.0, 0.75, 0.75, -0.0, 0.50, 0.0],
                [-0.0, -0.75, 0.75, -0.0, 0.50, 0.0],
                [0.0, 0.75, -0.75, -0.0, 0.50, 0.0],
                [-0.0, -0.75, -0.75, -0.0, 0.50, 0.0],
                [0.0, 0.75, 0.75, 0.0, -0.50, 0.0],
                [-0.0, -0.75, 0.75, 0.0, -0.50, 0.0],
                [0.0, 0.75, -0.75, 0.0, -0.50, 0.0],
                [-0.0, -0.75, -0.75, 0.0, -0.50, 0.0],
                [0.75, -0.0, 0.0, 0.75, 0.50, -0.0],
                [-0.75, -0.0, 0.0, 0.75, 0.50, -0.0],
                [0.75, 0.0, -0.0, -0.75, 0.50, -0.0],
                [-0.75, 0.0, -0.0, -0.75, 0.50, -0.0],
                [0.75, -0.0, 0.0, 0.75, -0.50, -0.0],
                [-0.75, -0.0, 0.0, 0.75, -0.50, -0.0],
                [0.75, 0.0, -0.0, -0.75, -0.50, -0.0],
                [-0.75, 0.0, -0.0, -0.75, -0.50, -0.0],
                [-0.0, 0.75, 0.0, 0.75, 0.50, 0.0],
                [0.0, -0.75, 0.0, 0.75, 0.50, 0.0],
                [-0.0, 0.75, -0.0, -0.75, 0.50, 0.0],
                [0.0, -0.75, -0.0, -0.75, 0.50, 0.0],
                [-0.0, 0.75, 0.0, 0.75, -0.50, 0.0],
                [0.0, -0.75, 0.0, 0.75, -0.50, 0.0],
                [-0.0, 0.75, -0.0, -0.75, -0.50, 0.0],
                [0.0, -0.75, -0.0, -0.75, -0.50, 0.0],
                [0.0, -0.0, 0.75, 0.75, 0.50, -0.0],
                [-0.0, 0.0, -0.75, 0.75, 0.50, -0.0],
                [0.0, -0.0, 0.75, -0.75, 0.50, -0.0],
                [-0.0, 0.0, -0.75, -0.75, 0.50, -0.0],
                [0.0, -0.0, 0.75, 0.75, -0.50, -0.0],
                [-0.0, 0.0, -0.75, 0.75, -0.50, -0.0],
                [0.0, -0.0, 0.75, -0.75, -0.50, -0.0],
                [-0.0, 0.0, -0.75, -0.75, -0.50, -0.0],
                [0.75, 0.50, -0.0, 0.0, 0.75, 0.0],
                [-0.75, 0.50, -0.0, 0.0, 0.75, 0.0],
                [0.75, -0.50, -0.0, 0.0, 0.75, 0.0],
                [-0.75, -0.50, -0.0, 0.0, 0.75, 0.0],
                [0.75, 0.50, 0.0, -0.0, -0.75, 0.0],
                [-0.75, 0.50, 0.0, -0.0, -0.75, 0.0],
                [0.75, -0.50, 0.0, -0.0, -0.75, 0.0],
                [-0.75, -0.50, 0.0, -0.0, -0.75, 0.0],
                [0.50, 0.75, -0.0, 0.0, 0.75, -0.0],
                [-0.50, 0.75, -0.0, 0.0, 0.75, -0.0],
                [0.50, -0.75, -0.0, 0.0, 0.75, -0.0],
                [-0.50, -0.75, -0.0, 0.0, 0.75, -0.0],
                [0.50, 0.75, 0.0, -0.0, -0.75, -0.0],
                [-0.50, 0.75, 0.0, -0.0, -0.75, -0.0],
                [0.50, -0.75, 0.0, -0.0, -0.75, -0.0],
                [-0.50, -0.75, 0.0, -0.0, -0.75, -0.0],
                [0.75, -0.0, 0.50, 0.0, 0.75, 0.0],
                [-0.75, -0.0, 0.50, 0.0, 0.75, 0.0],
                [0.75, 0.0, -0.50, 0.0, 0.75, 0.0],
                [-0.75, 0.0, -0.50, 0.0, 0.75, 0.0],
                [0.75, -0.0, 0.50, -0.0, -0.75, 0.0],
                [-0.75, -0.0, 0.50, -0.0, -0.75, 0.0],
                [0.75, 0.0, -0.50, -0.0, -0.75, 0.0],
                [-0.75, 0.0, -0.50, -0.0, -0.75, 0.0],
                [-0.0, 0.75, 0.50, 0.0, 0.75, -0.0],
                [0.0, -0.75, 0.50, 0.0, 0.75, -0.0],
                [-0.0, 0.75, -0.50, 0.0, 0.75, -0.0],
                [0.0, -0.75, -0.50, 0.0, 0.75, -0.0],
                [-0.0, 0.75, 0.50, -0.0, -0.75, -0.0],
                [0.0, -0.75, 0.50, -0.0, -0.75, -0.0],
                [-0.0, 0.75, -0.50, -0.0, -0.75, -0.0],
                [0.0, -0.75, -0.50, -0.0, -0.75, -0.0],
                [0.50, -0.0, 0.75, 0.0, 0.75, 0.0],
                [-0.50, -0.0, 0.75, 0.0, 0.75, 0.0],
                [0.50, 0.0, -0.75, 0.0, 0.75, 0.0],
                [-0.50, 0.0, -0.75, 0.0, 0.75, 0.0],
                [0.50, -0.0, 0.75, -0.0, -0.75, 0.0],
                [-0.50, -0.0, 0.75, -0.0, -0.75, 0.0],
                [0.50, 0.0, -0.75, -0.0, -0.75, 0.0],
                [-0.50, 0.0, -0.75, -0.0, -0.75, 0.0],
                [-0.0, 0.50, 0.75, 0.0, 0.75, -0.0],
                [0.0, -0.50, 0.75, 0.0, 0.75, -0.0],
                [-0.0, 0.50, -0.75, 0.0, 0.75, -0.0],
                [0.0, -0.50, -0.75, 0.0, 0.75, -0.0],
                [-0.0, 0.50, 0.75, -0.0, -0.75, -0.0],
                [0.0, -0.50, 0.75, -0.0, -0.75, -0.0],
                [-0.0, 0.50, -0.75, -0.0, -0.75, -0.0],
                [0.0, -0.50, -0.75, -0.0, -0.75, -0.0],
                [0.75, 0.0, -0.0, 0.50, 0.75, 0.0],
                [-0.75, 0.0, -0.0, 0.50, 0.75, 0.0],
                [0.75, -0.0, 0.0, -0.50, 0.75, 0.0],
                [-0.75, -0.0, 0.0, -0.50, 0.75, 0.0],
                [0.75, 0.0, -0.0, 0.50, -0.75, 0.0],
                [-0.75, 0.0, -0.0, 0.50, -0.75, 0.0],
                [0.75, -0.0, 0.0, -0.50, -0.75, 0.0],
                [-0.75, -0.0, 0.0, -0.50, -0.75, 0.0],
                [0.0, 0.75, -0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.75, -0.0, 0.50, 0.75, -0.0],
                [0.0, 0.75, 0.0, -0.50, 0.75, -0.0],
                [-0.0, -0.75, 0.0, -0.50, 0.75, -0.0],
                [0.0, 0.75, -0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.75, -0.0, 0.50, -0.75, -0.0],
                [0.0, 0.75, 0.0, -0.50, -0.75, -0.0],
                [-0.0, -0.75, 0.0, -0.50, -0.75, -0.0],
                [-0.0, 0.0, 0.75, 0.50, 0.75, 0.0],
                [0.0, -0.0, -0.75, 0.50, 0.75, 0.0],
                [-0.0, 0.0, 0.75, -0.50, 0.75, 0.0],
                [0.0, -0.0, -0.75, -0.50, 0.75, 0.0],
                [-0.0, 0.0, 0.75, 0.50, -0.75, 0.0],
                [0.0, -0.0, -0.75, 0.50, -0.75, 0.0],
                [-0.0, 0.0, 0.75, -0.50, -0.75, 0.0],
                [0.0, -0.0, -0.75, -0.50, -0.75, 0.0],
                [0.50, 0.0, -0.0, 0.75, 0.75, -0.0],
                [-0.50, 0.0, -0.0, 0.75, 0.75, -0.0],
                [0.50, -0.0, 0.0, -0.75, 0.75, -0.0],
                [-0.50, -0.0, 0.0, -0.75, 0.75, -0.0],
                [0.50, 0.0, -0.0, 0.75, -0.75, -0.0],
                [-0.50, 0.0, -0.0, 0.75, -0.75, -0.0],
                [0.50, -0.0, 0.0, -0.75, -0.75, -0.0],
                [-0.50, -0.0, 0.0, -0.75, -0.75, -0.0],
                [0.0, 0.50, -0.0, 0.75, 0.75, 0.0],
                [-0.0, -0.50, -0.0, 0.75, 0.75, 0.0],
                [0.0, 0.50, 0.0, -0.75, 0.75, 0.0],
                [-0.0, -0.50, 0.0, -0.75, 0.75, 0.0],
                [0.0, 0.50, -0.0, 0.75, -0.75, 0.0],
                [-0.0, -0.50, -0.0, 0.75, -0.75, 0.0],
                [0.0, 0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.0, -0.50, 0.0, -0.75, -0.75, 0.0],
                [-0.0, 0.0, 0.50, 0.75, 0.75, -0.0],
                [0.0, -0.0, -0.50, 0.75, 0.75, -0.0],
                [-0.0, 0.0, 0.50, -0.75, 0.75, -0.0],
                [0.0, -0.0, -0.50, -0.75, 0.75, -0.0],
                [-0.0, 0.0, 0.50, 0.75, -0.75, -0.0],
                [0.0, -0.0, -0.50, 0.75, -0.75, -0.0],
                [-0.0, 0.0, 0.50, -0.75, -0.75, -0.0],
                [0.0, -0.0, -0.50, -0.75, -0.75, -0.0],
                [0.75, 0.75, 0.0, 0.0, -0.0, 0.50],
                [-0.75, 0.75, 0.0, 0.0, -0.0, 0.50],
                [0.75, -0.75, 0.0, 0.0, -0.0, 0.50],
                [-0.75, -0.75, 0.0, 0.0, -0.0, 0.50],
                [0.75, 0.75, -0.0, -0.0, 0.0, -0.50],
                [-0.75, 0.75, -0.0, -0.0, 0.0, -0.50],
                [0.75, -0.75, -0.0, -0.0, 0.0, -0.50],
                [-0.75, -0.75, -0.0, -0.0, 0.0, -0.50],
                [0.75, 0.0, 0.75, 0.0, -0.0, 0.50],
                [-0.75, 0.0, 0.75, 0.0, -0.0, 0.50],
                [0.75, -0.0, -0.75, 0.0, -0.0, 0.50],
                [-0.75, -0.0, -0.75, 0.0, -0.0, 0.50],
                [0.75, 0.0, 0.75, -0.0, 0.0, -0.50],
                [-0.75, 0.0, 0.75, -0.0, 0.0, -0.50],
                [0.75, -0.0, -0.75, -0.0, 0.0, -0.50],
                [-0.75, -0.0, -0.75, -0.0, 0.0, -0.50],
                [0.0, 0.75, 0.75, 0.0, -0.0, 0.50],
                [-0.0, -0.75, 0.75, 0.0, -0.0, 0.50],
                [0.0, 0.75, -0.75, 0.0, -0.0, 0.50],
                [-0.0, -0.75, -0.75, 0.0, -0.0, 0.50],
                [0.0, 0.75, 0.75, -0.0, 0.0, -0.50],
                [-0.0, -0.75, 0.75, -0.0, 0.0, -0.50],
                [0.0, 0.75, -0.75, -0.0, 0.0, -0.50],
                [-0.0, -0.75, -0.75, -0.0, 0.0, -0.50],
                [0.75, 0.0, 0.0, 0.75, -0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.75, -0.0, 0.50],
                [0.75, -0.0, -0.0, -0.75, -0.0, 0.50],
                [-0.75, -0.0, -0.0, -0.75, -0.0, 0.50],
                [0.75, 0.0, 0.0, 0.75, 0.0, -0.50],
                [-0.75, 0.0, 0.0, 0.75, 0.0, -0.50],
                [0.75, -0.0, -0.0, -0.75, 0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.75, 0.0, -0.50],
                [0.0, 0.75, 0.0, 0.75, -0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.75, -0.0, 0.50],
                [0.0, 0.75, -0.0, -0.75, -0.0, 0.50],
                [-0.0, -0.75, -0.0, -0.75, -0.0, 0.50],
                [0.0, 0.75, 0.0, 0.75, 0.0, -0.50],
                [-0.0, -0.75, 0.0, 0.75, 0.0, -0.50],
                [0.0, 0.75, -0.0, -0.75, 0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.75, 0.0, -0.50],
                [0.0, 0.0, 0.75, 0.75, -0.0, 0.50],
                [-0.0, -0.0, -0.75, 0.75, -0.0, 0.50],
                [0.0, 0.0, 0.75, -0.75, -0.0, 0.50],
                [-0.0, -0.0, -0.75, -0.75, -0.0, 0.50],
                [0.0, 0.0, 0.75, 0.75, 0.0, -0.50],
                [-0.0, -0.0, -0.75, 0.75, 0.0, -0.50],
                [0.0, 0.0, 0.75, -0.75, 0.0, -0.50],
                [-0.0, -0.0, -0.75, -0.75, 0.0, -0.50],
                [0.75, -0.0, 0.0, 0.0, 0.75, 0.50],
                [-0.75, -0.0, 0.0, 0.0, 0.75, 0.50],
                [0.75, 0.0, -0.0, -0.0, -0.75, 0.50],
                [-0.75, 0.0, -0.0, -0.0, -0.75, 0.50],
                [0.75, -0.0, 0.0, 0.0, 0.75, -0.50],
                [-0.75, -0.0, 0.0, 0.0, 0.75, -0.50],
                [0.75, 0.0, -0.0, -0.0, -0.75, -0.50],
                [-0.75, 0.0, -0.0, -0.0, -0.75, -0.50],
                [-0.0, 0.75, 0.0, 0.0, 0.75, 0.50],
                [0.0, -0.75, 0.0, 0.0, 0.75, 0.50],
                [-0.0, 0.75, -0.0, -0.0, -0.75, 0.50],
                [0.0, -0.75, -0.0, -0.0, -0.75, 0.50],
                [-0.0, 0.75, 0.0, 0.0, 0.75, -0.50],
                [0.0, -0.75, 0.0, 0.0, 0.75, -0.50],
                [-0.0, 0.75, -0.0, -0.0, -0.75, -0.50],
                [0.0, -0.75, -0.0, -0.0, -0.75, -0.50],
                [0.0, -0.0, 0.75, 0.0, 0.75, 0.50],
                [-0.0, 0.0, -0.75, 0.0, 0.75, 0.50],
                [0.0, -0.0, 0.75, -0.0, -0.75, 0.50],
                [-0.0, 0.0, -0.75, -0.0, -0.75, 0.50],
                [0.0, -0.0, 0.75, 0.0, 0.75, -0.50],
                [-0.0, 0.0, -0.75, 0.0, 0.75, -0.50],
                [0.0, -0.0, 0.75, -0.0, -0.75, -0.50],
                [-0.0, 0.0, -0.75, -0.0, -0.75, -0.50],
                [0.0, -0.0, 0.0, 0.75, 0.75, 0.50],
                [-0.0, 0.0, -0.0, -0.75, 0.75, 0.50],
                [0.0, -0.0, 0.0, 0.75, -0.75, 0.50],
                [-0.0, 0.0, -0.0, -0.75, -0.75, 0.50],
                [0.0, -0.0, 0.0, 0.75, 0.75, -0.50],
                [-0.0, 0.0, -0.0, -0.75, 0.75, -0.50],
                [0.0, -0.0, 0.0, 0.75, -0.75, -0.50],
                [-0.0, 0.0, -0.0, -0.75, -0.75, -0.50],
                [0.75, 0.50, 0.0, -0.0, 0.0, 0.75],
                [-0.75, 0.50, 0.0, -0.0, 0.0, 0.75],
                [0.75, -0.50, 0.0, -0.0, 0.0, 0.75],
                [-0.75, -0.50, 0.0, -0.0, 0.0, 0.75],
                [0.75, 0.50, -0.0, 0.0, -0.0, -0.75],
                [-0.75, 0.50, -0.0, 0.0, -0.0, -0.75],
                [0.75, -0.50, -0.0, 0.0, -0.0, -0.75],
                [-0.75, -0.50, -0.0, 0.0, -0.0, -0.75],
                [0.50, 0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.50, 0.75, 0.0, -0.0, 0.0, 0.75],
                [0.50, -0.75, 0.0, -0.0, 0.0, 0.75],
                [-0.50, -0.75, 0.0, -0.0, 0.0, 0.75],
                [0.50, 0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.50, 0.75, -0.0, 0.0, -0.0, -0.75],
                [0.50, -0.75, -0.0, 0.0, -0.0, -0.75],
                [-0.50, -0.75, -0.0, 0.0, -0.0, -0.75],
                [0.75, 0.0, 0.50, -0.0, 0.0, 0.75],
                [-0.75, 0.0, 0.50, -0.0, 0.0, 0.75],
                [0.75, -0.0, -0.50, -0.0, 0.0, 0.75],
                [-0.75, -0.0, -0.50, -0.0, 0.0, 0.75],
                [0.75, 0.0, 0.50, 0.0, -0.0, -0.75],
                [-0.75, 0.0, 0.50, 0.0, -0.0, -0.75],
                [0.75, -0.0, -0.50, 0.0, -0.0, -0.75],
                [-0.75, -0.0, -0.50, 0.0, -0.0, -0.75],
                [0.0, 0.75, 0.50, -0.0, 0.0, 0.75],
                [-0.0, -0.75, 0.50, -0.0, 0.0, 0.75],
                [0.0, 0.75, -0.50, -0.0, 0.0, 0.75],
                [-0.0, -0.75, -0.50, -0.0, 0.0, 0.75],
                [0.0, 0.75, 0.50, 0.0, -0.0, -0.75],
                [-0.0, -0.75, 0.50, 0.0, -0.0, -0.75],
                [0.0, 0.75, -0.50, 0.0, -0.0, -0.75],
                [-0.0, -0.75, -0.50, 0.0, -0.0, -0.75],
                [0.50, 0.0, 0.75, -0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.75, -0.0, 0.0, 0.75],
                [0.50, -0.0, -0.75, -0.0, 0.0, 0.75],
                [-0.50, -0.0, -0.75, -0.0, 0.0, 0.75],
                [0.50, 0.0, 0.75, 0.0, -0.0, -0.75],
                [-0.50, 0.0, 0.75, 0.0, -0.0, -0.75],
                [0.50, -0.0, -0.75, 0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.75, 0.0, -0.0, -0.75],
                [0.0, 0.50, 0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.50, 0.75, -0.0, 0.0, 0.75],
                [0.0, 0.50, -0.75, -0.0, 0.0, 0.75],
                [-0.0, -0.50, -0.75, -0.0, 0.0, 0.75],
                [0.0, 0.50, 0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.50, 0.75, 0.0, -0.0, -0.75],
                [0.0, 0.50, -0.75, 0.0, -0.0, -0.75],
                [-0.0, -0.50, -0.75, 0.0, -0.0, -0.75],
                [0.75, -0.0, 0.0, 0.50, 0.0, 0.75],
                [-0.75, -0.0, 0.0, 0.50, 0.0, 0.75],
                [0.75, 0.0, -0.0, -0.50, 0.0, 0.75],
                [-0.75, 0.0, -0.0, -0.50, 0.0, 0.75],
                [0.75, -0.0, 0.0, 0.50, -0.0, -0.75],
                [-0.75, -0.0, 0.0, 0.50, -0.0, -0.75],
                [0.75, 0.0, -0.0, -0.50, -0.0, -0.75],
                [-0.75, 0.0, -0.0, -0.50, -0.0, -0.75],
                [-0.0, 0.75, 0.0, 0.50, 0.0, 0.75],
                [0.0, -0.75, 0.0, 0.50, 0.0, 0.75],
                [-0.0, 0.75, -0.0, -0.50, 0.0, 0.75],
                [0.0, -0.75, -0.0, -0.50, 0.0, 0.75],
                [-0.0, 0.75, 0.0, 0.50, -0.0, -0.75],
                [0.0, -0.75, 0.0, 0.50, -0.0, -0.75],
                [-0.0, 0.75, -0.0, -0.50, -0.0, -0.75],
                [0.0, -0.75, -0.0, -0.50, -0.0, -0.75],
                [0.0, -0.0, 0.75, 0.50, 0.0, 0.75],
                [-0.0, 0.0, -0.75, 0.50, 0.0, 0.75],
                [0.0, -0.0, 0.75, -0.50, 0.0, 0.75],
                [-0.0, 0.0, -0.75, -0.50, 0.0, 0.75],
                [0.0, -0.0, 0.75, 0.50, -0.0, -0.75],
                [-0.0, 0.0, -0.75, 0.50, -0.0, -0.75],
                [0.0, -0.0, 0.75, -0.50, -0.0, -0.75],
                [-0.0, 0.0, -0.75, -0.50, -0.0, -0.75],
                [0.50, -0.0, 0.0, 0.75, 0.0, 0.75],
                [-0.50, -0.0, 0.0, 0.75, 0.0, 0.75],
                [0.50, 0.0, -0.0, -0.75, 0.0, 0.75],
                [-0.50, 0.0, -0.0, -0.75, 0.0, 0.75],
                [0.50, -0.0, 0.0, 0.75, -0.0, -0.75],
                [-0.50, -0.0, 0.0, 0.75, -0.0, -0.75],
                [0.50, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.50, 0.0, -0.0, -0.75, -0.0, -0.75],
                [-0.0, 0.50, 0.0, 0.75, 0.0, 0.75],
                [0.0, -0.50, 0.0, 0.75, 0.0, 0.75],
                [-0.0, 0.50, -0.0, -0.75, 0.0, 0.75],
                [0.0, -0.50, -0.0, -0.75, 0.0, 0.75],
                [-0.0, 0.50, 0.0, 0.75, -0.0, -0.75],
                [0.0, -0.50, 0.0, 0.75, -0.0, -0.75],
                [-0.0, 0.50, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.50, -0.0, -0.75, -0.0, -0.75],
                [0.0, -0.0, 0.50, 0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.50, 0.75, 0.0, 0.75],
                [0.0, -0.0, 0.50, -0.75, 0.0, 0.75],
                [-0.0, 0.0, -0.50, -0.75, 0.0, 0.75],
                [0.0, -0.0, 0.50, 0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.50, 0.75, -0.0, -0.75],
                [0.0, -0.0, 0.50, -0.75, -0.0, -0.75],
                [-0.0, 0.0, -0.50, -0.75, -0.0, -0.75],
                [0.75, 0.0, -0.0, 0.0, 0.50, 0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.50, 0.75],
                [0.75, -0.0, 0.0, -0.0, -0.50, 0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.50, 0.75],
                [0.75, 0.0, -0.0, 0.0, 0.50, -0.75],
                [-0.75, 0.0, -0.0, 0.0, 0.50, -0.75],
                [0.75, -0.0, 0.0, -0.0, -0.50, -0.75],
                [-0.75, -0.0, 0.0, -0.0, -0.50, -0.75],
                [0.0, 0.75, -0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.50, 0.75],
                [0.0, 0.75, 0.0, -0.0, -0.50, 0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.50, 0.75],
                [0.0, 0.75, -0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.75, -0.0, 0.0, 0.50, -0.75],
                [0.0, 0.75, 0.0, -0.0, -0.50, -0.75],
                [-0.0, -0.75, 0.0, -0.0, -0.50, -0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.50, 0.75],
                [0.0, -0.0, -0.75, 0.0, 0.50, 0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.50, 0.75],
                [0.0, -0.0, -0.75, -0.0, -0.50, 0.75],
                [-0.0, 0.0, 0.75, 0.0, 0.50, -0.75],
                [0.0, -0.0, -0.75, 0.0, 0.50, -0.75],
                [-0.0, 0.0, 0.75, -0.0, -0.50, -0.75],
                [0.0, -0.0, -0.75, -0.0, -0.50, -0.75],
                [0.0, 0.0, -0.0, 0.75, 0.50, 0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.50, 0.75],
                [0.0, 0.0, -0.0, 0.75, -0.50, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.50, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.50, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.50, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.50, -0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.50, -0.75],
                [0.50, -0.0, 0.0, 0.0, 0.75, 0.75],
                [-0.50, -0.0, 0.0, 0.0, 0.75, 0.75],
                [0.50, 0.0, -0.0, -0.0, -0.75, 0.75],
                [-0.50, 0.0, -0.0, -0.0, -0.75, 0.75],
                [0.50, -0.0, 0.0, 0.0, 0.75, -0.75],
                [-0.50, -0.0, 0.0, 0.0, 0.75, -0.75],
                [0.50, 0.0, -0.0, -0.0, -0.75, -0.75],
                [-0.50, 0.0, -0.0, -0.0, -0.75, -0.75],
                [-0.0, 0.50, 0.0, 0.0, 0.75, 0.75],
                [0.0, -0.50, 0.0, 0.0, 0.75, 0.75],
                [-0.0, 0.50, -0.0, -0.0, -0.75, 0.75],
                [0.0, -0.50, -0.0, -0.0, -0.75, 0.75],
                [-0.0, 0.50, 0.0, 0.0, 0.75, -0.75],
                [0.0, -0.50, 0.0, 0.0, 0.75, -0.75],
                [-0.0, 0.50, -0.0, -0.0, -0.75, -0.75],
                [0.0, -0.50, -0.0, -0.0, -0.75, -0.75],
                [0.0, -0.0, 0.50, 0.0, 0.75, 0.75],
                [-0.0, 0.0, -0.50, 0.0, 0.75, 0.75],
                [0.0, -0.0, 0.50, -0.0, -0.75, 0.75],
                [-0.0, 0.0, -0.50, -0.0, -0.75, 0.75],
                [0.0, -0.0, 0.50, 0.0, 0.75, -0.75],
                [-0.0, 0.0, -0.50, 0.0, 0.75, -0.75],
                [0.0, -0.0, 0.50, -0.0, -0.75, -0.75],
                [-0.0, 0.0, -0.50, -0.0, -0.75, -0.75],
                [0.0, -0.0, 0.0, 0.50, 0.75, 0.75],
                [-0.0, 0.0, -0.0, -0.50, 0.75, 0.75],
                [0.0, -0.0, 0.0, 0.50, -0.75, 0.75],
                [-0.0, 0.0, -0.0, -0.50, -0.75, 0.75],
                [0.0, -0.0, 0.0, 0.50, 0.75, -0.75],
                [-0.0, 0.0, -0.0, -0.50, 0.75, -0.75],
                [0.0, -0.0, 0.0, 0.50, -0.75, -0.75],
                [-0.0, 0.0, -0.0, -0.50, -0.75, -0.75],
            ];

            let should_be = should_be.iter().map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1) * (N - 2));
        }

        {
            let vv = Generator::new([0.75f64, 0.5, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.50, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.50, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.50, 0.0, 0.0, 0.0, 0.0],
                [-0.75, -0.50, 0.0, 0.0, 0.0, 0.0],
                [0.50, 0.75, -0.0, -0.0, -0.0, -0.0],
                [-0.50, 0.75, -0.0, -0.0, -0.0, -0.0],
                [0.50, -0.75, -0.0, -0.0, -0.0, -0.0],
                [-0.50, -0.75, -0.0, -0.0, -0.0, -0.0],
                [0.75, 0.0, 0.50, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.50, 0.0, 0.0, 0.0],
                [0.75, -0.0, -0.50, 0.0, 0.0, 0.0],
                [-0.75, -0.0, -0.50, 0.0, 0.0, 0.0],
                [0.0, 0.75, 0.50, -0.0, -0.0, -0.0],
                [-0.0, -0.75, 0.50, -0.0, -0.0, -0.0],
                [0.0, 0.75, -0.50, -0.0, -0.0, -0.0],
                [-0.0, -0.75, -0.50, -0.0, -0.0, -0.0],
                [0.50, 0.0, 0.75, 0.0, 0.0, 0.0],
                [-0.50, 0.0, 0.75, 0.0, 0.0, 0.0],
                [0.50, -0.0, -0.75, 0.0, 0.0, 0.0],
                [-0.50, -0.0, -0.75, 0.0, 0.0, 0.0],
                [0.0, 0.50, 0.75, -0.0, -0.0, -0.0],
                [-0.0, -0.50, 0.75, -0.0, -0.0, -0.0],
                [0.0, 0.50, -0.75, -0.0, -0.0, -0.0],
                [-0.0, -0.50, -0.75, -0.0, -0.0, -0.0],
                [0.75, 0.0, 0.0, 0.50, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.50, 0.0, 0.0],
                [0.75, -0.0, -0.0, -0.50, 0.0, 0.0],
                [-0.75, -0.0, -0.0, -0.50, 0.0, 0.0],
                [0.0, 0.75, 0.0, 0.50, -0.0, -0.0],
                [-0.0, -0.75, 0.0, 0.50, -0.0, -0.0],
                [0.0, 0.75, -0.0, -0.50, -0.0, -0.0],
                [-0.0, -0.75, -0.0, -0.50, -0.0, -0.0],
                [0.0, 0.0, 0.75, 0.50, 0.0, 0.0],
                [-0.0, -0.0, -0.75, 0.50, 0.0, 0.0],
                [0.0, 0.0, 0.75, -0.50, 0.0, 0.0],
                [-0.0, -0.0, -0.75, -0.50, 0.0, 0.0],
                [0.50, 0.0, 0.0, 0.75, -0.0, -0.0],
                [-0.50, 0.0, 0.0, 0.75, -0.0, -0.0],
                [0.50, -0.0, -0.0, -0.75, -0.0, -0.0],
                [-0.50, -0.0, -0.0, -0.75, -0.0, -0.0],
                [0.0, 0.50, 0.0, 0.75, 0.0, 0.0],
                [-0.0, -0.50, 0.0, 0.75, 0.0, 0.0],
                [0.0, 0.50, -0.0, -0.75, 0.0, 0.0],
                [-0.0, -0.50, -0.0, -0.75, 0.0, 0.0],
                [0.0, 0.0, 0.50, 0.75, -0.0, -0.0],
                [-0.0, -0.0, -0.50, 0.75, -0.0, -0.0],
                [0.0, 0.0, 0.50, -0.75, -0.0, -0.0],
                [-0.0, -0.0, -0.50, -0.75, -0.0, -0.0],
                [0.75, 0.0, 0.0, 0.0, 0.50, 0.0],
                [-0.75, 0.0, 0.0, 0.0, 0.50, 0.0],
                [0.75, -0.0, -0.0, -0.0, -0.50, 0.0],
                [-0.75, -0.0, -0.0, -0.0, -0.50, 0.0],
                [0.0, 0.75, 0.0, 0.0, 0.50, -0.0],
                [-0.0, -0.75, 0.0, 0.0, 0.50, -0.0],
                [0.0, 0.75, -0.0, -0.0, -0.50, -0.0],
                [-0.0, -0.75, -0.0, -0.0, -0.50, -0.0],
                [0.0, 0.0, 0.75, 0.0, 0.50, 0.0],
                [-0.0, -0.0, -0.75, 0.0, 0.50, 0.0],
                [0.0, 0.0, 0.75, -0.0, -0.50, 0.0],
                [-0.0, -0.0, -0.75, -0.0, -0.50, 0.0],
                [0.0, 0.0, 0.0, 0.75, 0.50, -0.0],
                [-0.0, -0.0, -0.0, -0.75, 0.50, -0.0],
                [0.0, 0.0, 0.0, 0.75, -0.50, -0.0],
                [-0.0, -0.0, -0.0, -0.75, -0.50, -0.0],
                [0.50, 0.0, 0.0, 0.0, 0.75, 0.0],
                [-0.50, 0.0, 0.0, 0.0, 0.75, 0.0],
                [0.50, -0.0, -0.0, -0.0, -0.75, 0.0],
                [-0.50, -0.0, -0.0, -0.0, -0.75, 0.0],
                [0.0, 0.50, 0.0, 0.0, 0.75, -0.0],
                [-0.0, -0.50, 0.0, 0.0, 0.75, -0.0],
                [0.0, 0.50, -0.0, -0.0, -0.75, -0.0],
                [-0.0, -0.50, -0.0, -0.0, -0.75, -0.0],
                [0.0, 0.0, 0.50, 0.0, 0.75, 0.0],
                [-0.0, -0.0, -0.50, 0.0, 0.75, 0.0],
                [0.0, 0.0, 0.50, -0.0, -0.75, 0.0],
                [-0.0, -0.0, -0.50, -0.0, -0.75, 0.0],
                [0.0, 0.0, 0.0, 0.50, 0.75, -0.0],
                [-0.0, -0.0, -0.0, -0.50, 0.75, -0.0],
                [0.0, 0.0, 0.0, 0.50, -0.75, -0.0],
                [-0.0, -0.0, -0.0, -0.50, -0.75, -0.0],
                [0.75, 0.0, 0.0, 0.0, 0.0, 0.50],
                [-0.75, 0.0, 0.0, 0.0, 0.0, 0.50],
                [0.75, -0.0, -0.0, -0.0, -0.0, -0.50],
                [-0.75, -0.0, -0.0, -0.0, -0.0, -0.50],
                [0.0, 0.75, 0.0, 0.0, 0.0, 0.50],
                [-0.0, -0.75, 0.0, 0.0, 0.0, 0.50],
                [0.0, 0.75, -0.0, -0.0, -0.0, -0.50],
                [-0.0, -0.75, -0.0, -0.0, -0.0, -0.50],
                [0.0, 0.0, 0.75, 0.0, 0.0, 0.50],
                [-0.0, -0.0, -0.75, 0.0, 0.0, 0.50],
                [0.0, 0.0, 0.75, -0.0, -0.0, -0.50],
                [-0.0, -0.0, -0.75, -0.0, -0.0, -0.50],
                [0.0, 0.0, 0.0, 0.75, 0.0, 0.50],
                [-0.0, -0.0, -0.0, -0.75, 0.0, 0.50],
                [0.0, 0.0, 0.0, 0.75, -0.0, -0.50],
                [-0.0, -0.0, -0.0, -0.75, -0.0, -0.50],
                [0.0, 0.0, 0.0, 0.0, 0.75, 0.50],
                [-0.0, -0.0, -0.0, -0.0, -0.75, 0.50],
                [0.0, 0.0, 0.0, 0.0, 0.75, -0.50],
                [-0.0, -0.0, -0.0, -0.0, -0.75, -0.50],
                [0.50, 0.0, 0.0, 0.0, 0.0, 0.75],
                [-0.50, 0.0, 0.0, 0.0, 0.0, 0.75],
                [0.50, -0.0, -0.0, -0.0, -0.0, -0.75],
                [-0.50, -0.0, -0.0, -0.0, -0.0, -0.75],
                [0.0, 0.50, 0.0, 0.0, 0.0, 0.75],
                [-0.0, -0.50, 0.0, 0.0, 0.0, 0.75],
                [0.0, 0.50, -0.0, -0.0, -0.0, -0.75],
                [-0.0, -0.50, -0.0, -0.0, -0.0, -0.75],
                [0.0, 0.0, 0.50, 0.0, 0.0, 0.75],
                [-0.0, -0.0, -0.50, 0.0, 0.0, 0.75],
                [0.0, 0.0, 0.50, -0.0, -0.0, -0.75],
                [-0.0, -0.0, -0.50, -0.0, -0.0, -0.75],
                [0.0, 0.0, 0.0, 0.50, 0.0, 0.75],
                [-0.0, -0.0, -0.0, -0.50, 0.0, 0.75],
                [0.0, 0.0, 0.0, 0.50, -0.0, -0.75],
                [-0.0, -0.0, -0.0, -0.50, -0.0, -0.75],
                [0.0, 0.0, 0.0, 0.0, 0.50, 0.75],
                [-0.0, -0.0, -0.0, -0.0, -0.50, 0.75],
                [0.0, 0.0, 0.0, 0.0, 0.50, -0.75],
                [-0.0, -0.0, -0.0, -0.0, -0.50, -0.75],
            ]
            .map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 4 * N * (N - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.75, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.75, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.75, 0.0, 0.0, 0.0, 0.0],
                [-0.75, -0.75, 0.0, 0.0, 0.0, 0.0],
                [0.75, -0.0, 0.75, -0.0, -0.0, -0.0],
                [-0.75, -0.0, 0.75, -0.0, -0.0, -0.0],
                [0.75, 0.0, -0.75, -0.0, -0.0, -0.0],
                [-0.75, 0.0, -0.75, -0.0, -0.0, -0.0],
                [-0.0, 0.75, 0.75, 0.0, 0.0, 0.0],
                [0.0, -0.75, 0.75, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.75, 0.0, 0.0, 0.0],
                [0.0, -0.75, -0.75, 0.0, 0.0, 0.0],
                [0.75, -0.0, -0.0, 0.75, -0.0, -0.0],
                [-0.75, -0.0, -0.0, 0.75, -0.0, -0.0],
                [0.75, 0.0, 0.0, -0.75, -0.0, -0.0],
                [-0.75, 0.0, 0.0, -0.75, -0.0, -0.0],
                [-0.0, 0.75, -0.0, 0.75, 0.0, 0.0],
                [0.0, -0.75, -0.0, 0.75, 0.0, 0.0],
                [-0.0, 0.75, 0.0, -0.75, 0.0, 0.0],
                [0.0, -0.75, 0.0, -0.75, 0.0, 0.0],
                [-0.0, -0.0, 0.75, 0.75, -0.0, -0.0],
                [0.0, 0.0, -0.75, 0.75, -0.0, -0.0],
                [-0.0, -0.0, 0.75, -0.75, -0.0, -0.0],
                [0.0, 0.0, -0.75, -0.75, -0.0, -0.0],
                [0.75, 0.0, -0.0, -0.0, 0.75, 0.0],
                [-0.75, 0.0, -0.0, -0.0, 0.75, 0.0],
                [0.75, -0.0, 0.0, 0.0, -0.75, 0.0],
                [-0.75, -0.0, 0.0, 0.0, -0.75, 0.0],
                [0.0, 0.75, -0.0, -0.0, 0.75, -0.0],
                [-0.0, -0.75, -0.0, -0.0, 0.75, -0.0],
                [0.0, 0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.0, -0.75, 0.0, 0.0, -0.75, -0.0],
                [-0.0, 0.0, 0.75, -0.0, 0.75, 0.0],
                [0.0, -0.0, -0.75, -0.0, 0.75, 0.0],
                [-0.0, 0.0, 0.75, 0.0, -0.75, 0.0],
                [0.0, -0.0, -0.75, 0.0, -0.75, 0.0],
                [-0.0, 0.0, -0.0, 0.75, 0.75, -0.0],
                [0.0, -0.0, 0.0, -0.75, 0.75, -0.0],
                [-0.0, 0.0, -0.0, 0.75, -0.75, -0.0],
                [0.0, -0.0, 0.0, -0.75, -0.75, -0.0],
                [0.75, 0.0, -0.0, 0.0, -0.0, 0.75],
                [-0.75, 0.0, -0.0, 0.0, -0.0, 0.75],
                [0.75, -0.0, 0.0, -0.0, 0.0, -0.75],
                [-0.75, -0.0, 0.0, -0.0, 0.0, -0.75],
                [0.0, 0.75, -0.0, 0.0, -0.0, 0.75],
                [-0.0, -0.75, -0.0, 0.0, -0.0, 0.75],
                [0.0, 0.75, 0.0, -0.0, 0.0, -0.75],
                [-0.0, -0.75, 0.0, -0.0, 0.0, -0.75],
                [-0.0, 0.0, 0.75, 0.0, -0.0, 0.75],
                [0.0, -0.0, -0.75, 0.0, -0.0, 0.75],
                [-0.0, 0.0, 0.75, -0.0, 0.0, -0.75],
                [0.0, -0.0, -0.75, -0.0, 0.0, -0.75],
                [0.0, 0.0, -0.0, 0.75, -0.0, 0.75],
                [-0.0, -0.0, 0.0, -0.75, -0.0, 0.75],
                [0.0, 0.0, -0.0, 0.75, 0.0, -0.75],
                [-0.0, -0.0, 0.0, -0.75, 0.0, -0.75],
                [-0.0, -0.0, 0.0, 0.0, 0.75, 0.75],
                [0.0, 0.0, -0.0, -0.0, -0.75, 0.75],
                [-0.0, -0.0, 0.0, 0.0, 0.75, -0.75],
                [0.0, 0.0, -0.0, -0.0, -0.75, -0.75],
            ]
            .map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * N * (N - 1));
        }

        {
            let vv = Generator::new([0.75f64, 0.0, 0.0, 0.0, 0.0, 0.0]);

            let should_be = [
                [0.75, 0.0, 0.0, 0.0, 0.0, 0.0],
                [-0.75, 0.0, 0.0, 0.0, 0.0, 0.0],
                [-0.0, 0.75, -0.0, -0.0, -0.0, -0.0],
                [0.0, -0.75, -0.0, -0.0, -0.0, -0.0],
                [0.0, -0.0, 0.75, 0.0, 0.0, 0.0],
                [-0.0, 0.0, -0.75, 0.0, 0.0, 0.0],
                [-0.0, -0.0, 0.0, 0.75, -0.0, -0.0],
                [0.0, 0.0, -0.0, -0.75, -0.0, -0.0],
                [0.0, 0.0, -0.0, -0.0, 0.75, 0.0],
                [-0.0, -0.0, 0.0, 0.0, -0.75, 0.0],
                [-0.0, -0.0, -0.0, 0.0, 0.0, 0.75],
                [0.0, 0.0, 0.0, -0.0, -0.0, -0.75],
            ]
            .map(|[a, b, c, d, e, f]| {
                [
                    CV + a * HWV,
                    CV + b * HWV,
                    CV + c * HWV,
                    CV + d * HWV,
                    CV + e * HWV,
                    CV + f * HWV,
                ]
            });

            let mut count = 0;
            for (a, b) in vv.point_permutations(&centre, &half_widths).zip(should_be) {
                count += 1;
                assert!((a[0] - b[0]).abs() < f64::EPSILON);
                assert!((a[1] - b[1]).abs() < f64::EPSILON);
                assert!((a[2] - b[2]).abs() < f64::EPSILON);
                assert!((a[3] - b[3]).abs() < f64::EPSILON);
                assert!((a[4] - b[4]).abs() < f64::EPSILON);
                assert!((a[5] - b[5]).abs() < f64::EPSILON);
            }

            assert_eq!(count, 2 * N);
        }
    }
}