cryspglib 0.1.0

//! Hall 符号匹配。
//!
//! 将原胞的对称操作与 Hall 符号数据库 ([`spg_database`](crate::spg_database)) 比对，
//! 找出一组候选的 Hall 编号，供后续空间群搜索使用。
//!
//! Hall 编号 (1–530) 比空间群编号 (1–230) 更精细，每个 Hall 符号对应
//! 唯一的空间群 + 原点设置组合。
// Generated by convert_hall_final.py

use crate::cell::{cel_is_overlap, cel_layer_is_overlap, AperiodicAxis};
use crate::debug;
use crate::mathfunc::{
    Mat3, Mat3I, Vec3, mat_cast_matrix_3i_to_3d, mat_check_identity_matrix_i3,
    mat_dmod1, mat_get_determinant_i3, mat_get_similar_matrix_d3, mat_multiply_matrix_d3,
    mat_multiply_matrix_vector_d3, mat_multiply_matrix_vector_id3,
};
use crate::spg_database::{Centering, spgdb_get_operation_index, spgdb_get_operation_by_index};
use crate::symmetry::Symmetry;

// ============================================================================
// Constants & Static Data
// ============================================================================
static M_RC_INV: [[f64; 3]; 3] = [
    [0.6666666666666666, -0.3333333333333333, -0.3333333333333333],
    [0.3333333333333333, 0.3333333333333333, -0.6666666666666666],
    [0.3333333333333333, 0.3333333333333333, 0.3333333333333333]];

static M_CC_INV: [[f64; 3]; 3] = [
    [0.5, 0.5, 0.0],
    [-0.5, 0.5, 0.0],
    [0.0, 0.0, 1.0]];

static M_BC_INV: [[f64; 3]; 3] = [
    [0.5, 0.0, -0.5],
    [0.0, 1.0, 0.0],
    [0.5, 0.0, 0.5]];

static M_AC_INV: [[f64; 3]; 3] = [
    [1.0, 0.0, 0.0],
    [0.0, 0.5, -0.5],
    [0.0, 0.5, 0.5]];

static M_FCC_INV: [[f64; 3]; 3] = [
    [0.0, 0.5, 0.5],
    [0.5, 0.0, 0.5],
    [0.5, 0.5, 0.0]];

static M_BCC_INV: [[f64; 3]; 3] = [
    [-0.5, 0.5, 0.5],
    [0.5, -0.5, 0.5],
    [0.5, 0.5, -0.5]];

static M_RC: [[i32; 3]; 3] = [
    [1, 0, 1],
    [-1, 1, 1],
    [0, -1, 1]];

static M_CC: [[i32; 3]; 3] = [
    [1, -1, 0],
    [1, 1, 0],
    [0, 0, 1]];

static M_BC: [[i32; 3]; 3] = [
    [1, 0, 1],
    [0, 1, 0],
    [-1, 0, 1]];

static M_AC: [[i32; 3]; 3] = [
    [1, 0, 0],
    [0, 1, 1],
    [0, -1, 1]];

static M_FCC: [[i32; 3]; 3] = [
    [-1, 1, 1],
    [1, -1, 1],
    [1, 1, -1]];

static M_BCC: [[i32; 3]; 3] = [
    [0, 1, 1],
    [1, 0, 1],
    [1, 1, 0]];

static TRICLI_VSPU: [[[f64; 9]; 3]; 2] = [
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static TRICLI_GENERATORS: [[[i32; 9]; 3]; 2] = [
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]]];

static MONOCLI_VSPU: [[[f64; 9]; 3]; 9] = [
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static MONOCLI_A_VSPU: [[[f64; 9]; 3]; 9] = [
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]]];

static MONOCLI_B_VSPU: [[[f64; 9]; 3]; 9] = [
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]]];

static MONOCLI_C_VSPU: [[[f64; 9]; 3]; 9] = [
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static MONOCLI_I_VSPU: [[[f64; 9]; 3]; 9] = [
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            -0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]]];

static MONOCLI_GENERATORS: [[[i32; 9]; 3]; 9] = [
    [
        
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]]];

static ORTHO_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static ORTHO_F_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            0.0,
            0.5,
            0.0,
            -0.25,
            -0.25,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            -0.25,
            -0.25,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            -0.25,
            0.75,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0]]];

static ORTHO_I_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            -1.0,
            0.0,
            0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]]];

static ORTHO_A_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static ORTHO_B_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0]]];

static ORTHO_C_VSPU: [[[f64; 9]; 3]; 5] = [
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static ORTHO_GENERATORS: [[[i32; 9]; 3]; 5] = [
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static TETRA_VSPU: [[[f64; 9]; 3]; 8] = [
    [
        
        [
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static TETRA_I_VSPU: [[[f64; 9]; 3]; 8] = [
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.75,
            0.25,
            0.25,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.25,
            -0.25,
            -0.25,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -1.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.75,
            0.25,
            0.0,
            0.0,
            0.25,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.25,
            -0.25,
            0.0,
            0.0,
            -0.25,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            2.0,
            0.0,
            -0.5,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.5,
            0.0,
            -0.5],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.5,
            0.0,
            -0.5],
        [
            1.0,
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0]]];

static TETRA_GENERATORS: [[[i32; 9]; 3]; 8] = [
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static TRIGO_VSPU: [[[f64; 9]; 3]; 13] = [
    [
        
        [
            -0.6666666666666666,
            0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.3333333333333333,
            -0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.3333333333333333,
            0.0,
            -0.6666666666666666,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.3333333333333333,
            0.0,
            -0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            -2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            -2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.3333333333333333,
            0.0,
            -0.6666666666666666,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.3333333333333333,
            0.0,
            -0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -6.0,
            3.0,
            0.0,
            4.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -3.0,
            1.0,
            0.0,
            2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            1.0,
            0.0,
            -2.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            -2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static TRIGO_GENERATORS: [[[i32; 9]; 3]; 13] = [
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static RHOMBO_H_VSPU: [[[f64; 9]; 3]; 8] = [
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -1.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            -1.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -1.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            1.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0]]];

static RHOMBO_H_GENERATORS: [[[i32; 9]; 3]; 8] = [
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static RHOMBO_P_VSPU: [[[f64; 9]; 3]; 8] = [
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -1.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            0.0,
            -1.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -1.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            1.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0]]];

static RHOMBO_P_GENERATORS: [[[i32; 9]; 3]; 8] = [
    [
        
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            -1,
            0,
            -1,
            0,
            -1,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            1,
            0,
            1,
            0,
            1,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            -1,
            0,
            -1,
            0,
            -1,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            1,
            0,
            1,
            0,
            1,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            -1,
            0,
            -1,
            0,
            -1,
            0,
            0],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static HEXA_VSPU: [[[f64; 9]; 3]; 8] = [
    [
        
        [
            -1.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.3333333333333333,
            -0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.3333333333333333,
            -0.6666666666666666,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.3333333333333333,
            0.0,
            0.0,
            -0.3333333333333333,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.3333333333333333,
            0.0,
            0.0,
            -0.6666666666666666,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]]];

static HEXA_GENERATORS: [[[i32; 9]; 3]; 8] = [
    [
        
        [
            1,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            -1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

static CUBIC_VSPU: [[[f64; 9]; 3]; 10] = [
    [
        
        [
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            0.5,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -0.5,
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -0.5,
            0.0,
            -1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.5,
            -0.5,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.5,
            0.5,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            -0.5,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.5,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.5,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            1.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0]]];

static CUBIC_F_VSPU: [[[f64; 9]; 3]; 10] = [
    [
        
        [
            0.0,
            0.0,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.5,
            -0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            -0.5,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.25,
            -0.25,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.75,
            -0.25,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.25,
            -0.25,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            -1.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -0.25,
            0.25,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.25,
            -0.75,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -0.25,
            0.25,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            -0.5,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            -0.5,
            0.0,
            -0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.5,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -0.5,
            0.0,
            0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.5,
            -0.5,
            0.0,
            0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.5,
            0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -0.5,
            -0.5,
            0.0,
            -0.5,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0]],
    [
        
        [
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            -1.0,
            -2.0,
            0.0,
            0.0,
            0.5,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -0.5,
            0.0,
            0.0]]];

static CUBIC_I_VSPU: [[[f64; 9]; 3]; 10] = [
    [
        
        [
            0.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            1.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            0.0,
            1.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            1.0,
            0.0,
            -1.0,
            -2.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -1.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            -1.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            3.0,
            0.0,
            -1.0,
            -3.0,
            0.0,
            2.0,
            0.0,
            0.0,
            0.0],
        [
            -3.0,
            0.0,
            1.0,
            3.0,
            0.0,
            -3.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            1.0,
            2.0,
            -5.0,
            -7.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            1.0,
            -4.0,
            -5.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            0.0,
            1.0,
            -2.0,
            -2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -2.0,
            1.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            -1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            2.0,
            -1.0,
            0.0,
            -2.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            1.0,
            0.0,
            0.0,
            0.0,
            -2.0,
            1.0,
            0.0,
            0.0,
            0.0],
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            1.0,
            -1.0,
            0.0,
            0.0,
            0.0],
        [
            1.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -2.0,
            -3.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            1.0,
            -1.0,
            1.0],
        [
            -1.0,
            -3.0,
            0.0,
            -1.0,
            0.0,
            0.0,
            1.0,
            -1.0,
            1.0],
        [
            0.0,
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0,
            0.0]],
    [
        
        [
            -1.0,
            0.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            0.0,
            -1.0,
            1.0],
        [
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            0.0,
            0.0,
            -1.0,
            1.0],
        [
            -1.0,
            0.0,
            0.0,
            1.0,
            0.0,
            -1.0,
            0.0,
            -1.0,
            1.0]]];

static CUBIC_GENERATORS: [[[i32; 9]; 3]; 10] = [
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            1,
            0,
            -1,
            0,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            1,
            0,
            0,
            0,
            1,
            0,
            0,
            0,
            -1],
        [
            0,
            0,
            -1,
            -1,
            0,
            0,
            0,
            -1,
            0],
        [
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0,
            0]],
    [
        
        [
            0,
            -1,
            0,
            1,
            0,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]],
    [
        
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            1],
        [
            0,
            0,
            1,
            1,
            0,
            0,
            0,
            1,
            0],
        [
            -1,
            0,
            0,
            0,
            -1,
            0,
            0,
            0,
            -1]]];

pub fn hal_match_hall_symbol_db(
    origin_shift: &mut Vec3,
    bravais_lattice: &Mat3,
    hall_number: i32,
    centering: Centering,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    find_hall_symbol(
        origin_shift,
        bravais_lattice,
        hall_number,
        centering,
        symmetry,
        symprec,
    )
}

// ============================================================================
// Internal Functions
// ============================================================================

fn find_hall_symbol(
    origin_shift: &mut Vec3,
    bravais_lattice: &Mat3,
    hall_number: i32,
    centering: Centering,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    let mut primitive_lattice = [[0.0; 3]; 3];

    match centering {
        Centering::Primitive => primitive_lattice = *bravais_lattice,
        Centering::Body => primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_BCC_INV),
        Centering::Face => primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_FCC_INV),
        Centering::AFace => primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_AC_INV),
        Centering::BFace => primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_BC_INV),
        Centering::CFace => primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_CC_INV),
        Centering::RCenter => {
            primitive_lattice = mat_multiply_matrix_d3(bravais_lattice, &M_RC_INV)
        }
        _ => {}
    }

    let mut found = false;

    if (489..=530).contains(&hall_number) {
        if is_hall_symbol_cubic(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            centering,
            symprec,
        ) {
            found = true;
        }
    } else if (462..=488).contains(&hall_number) || (-116..=-109).contains(&hall_number) {
        if is_hall_symbol_hexa(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            symprec,
        ) {
            found = true;
        }
    } else if (430..=461).contains(&hall_number) || (-108..=-101).contains(&hall_number) {
        if matches!(
            hall_number,
            433 | 434 | 436 | 437 | 444 | 445 | 450 | 451 | 452 | 453 | 458 | 459 | 460 | 461
        ) {
            if is_hall_symbol_rhombo(
                origin_shift,
                hall_number,
                &primitive_lattice,
                symmetry,
                symprec,
            ) {
                found = true;
            }
        } else {
            if is_hall_symbol_trigonal(
                origin_shift,
                hall_number,
                &primitive_lattice,
                symmetry,
                symprec,
            ) {
                found = true;
            }
        }
    } else if (349..=429).contains(&hall_number) || (-100..=-82).contains(&hall_number) {
        if is_hall_symbol_tetra(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            centering,
            symprec,
        ) {
            found = true;
        }
    } else if (108..=348).contains(&hall_number) || (-81..=-34).contains(&hall_number) {
        if is_hall_symbol_ortho(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            centering,
            symprec,
        ) {
            found = true;
        }
    } else if (3..=107).contains(&hall_number) || (-33..=-3).contains(&hall_number) {
        if is_hall_symbol_monocli(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            centering,
            symprec,
        ) {
            found = true;
        }
    } else if (-2..=2).contains(&hall_number) && hall_number != 0 {
        if is_hall_symbol_tricli(
            origin_shift,
            hall_number,
            &primitive_lattice,
            symmetry,
            symprec,
        ) {
            found = true;
        }
    }

    if found {
        match centering {
            Centering::Primitive => {}
            Centering::Body => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_BCC_INV, origin_shift)
            }
            Centering::Face => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_FCC_INV, origin_shift)
            }
            Centering::AFace => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_AC_INV, origin_shift)
            }
            Centering::BFace => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_BC_INV, origin_shift)
            }
            Centering::CFace => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_CC_INV, origin_shift)
            }
            Centering::RCenter => {
                *origin_shift = mat_multiply_matrix_vector_d3(&M_RC_INV, origin_shift)
            }
            _ => {}
        }
        return true;
    }

    false
}

fn is_hall_symbol_cubic(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    centering: Centering,
    symprec: f64,
) -> bool {
    for i in 0..10 {
        let (generators, vspu) = match centering {
            Centering::Primitive => (&CUBIC_GENERATORS[i], &CUBIC_VSPU[i]),
            Centering::Body => (&CUBIC_GENERATORS[i], &CUBIC_I_VSPU[i]),
            Centering::Face => (&CUBIC_GENERATORS[i], &CUBIC_F_VSPU[i]),
            _ => continue,
        };

        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            centering,
            generators,
            vspu,
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_hexa(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    for i in 0..8 {
        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            Centering::Primitive,
            &HEXA_GENERATORS[i],
            &HEXA_VSPU[i],
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_trigonal(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    for i in 0..13 {
        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            Centering::Primitive,
            &TRIGO_GENERATORS[i],
            &TRIGO_VSPU[i],
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_rhombo(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    if matches!(hall_number, 433 | 436 | 444 | 450 | 452 | 458 | 460) {
        for i in 0..8 {
            if is_hall_symbol(
                shift,
                hall_number,
                primitive_lattice,
                symmetry,
                Centering::RCenter,
                &RHOMBO_H_GENERATORS[i],
                &RHOMBO_H_VSPU[i],
                symprec,
            ) {
                return true;
            }
        }
    } else {
        for i in 0..8 {
            if is_hall_symbol(
                shift,
                hall_number,
                primitive_lattice,
                symmetry,
                Centering::Primitive,
                &RHOMBO_P_GENERATORS[i],
                &RHOMBO_P_VSPU[i],
                symprec,
            ) {
                return true;
            }
        }
    }
    false
}

fn is_hall_symbol_tetra(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    centering: Centering,
    symprec: f64,
) -> bool {
    for i in 0..8 {
        let (generators, vspu) = match centering {
            Centering::Primitive => (&TETRA_GENERATORS[i], &TETRA_VSPU[i]),
            Centering::Body => (&TETRA_GENERATORS[i], &TETRA_I_VSPU[i]),
            _ => continue,
        };

        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            centering,
            generators,
            vspu,
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_ortho(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    centering: Centering,
    symprec: f64,
) -> bool {
    for i in 0..5 {
        let (generators, vspu) = match centering {
            Centering::Primitive => (&ORTHO_GENERATORS[i], &ORTHO_VSPU[i]),
            Centering::Body => (&ORTHO_GENERATORS[i], &ORTHO_I_VSPU[i]),
            Centering::Face => (&ORTHO_GENERATORS[i], &ORTHO_F_VSPU[i]),
            Centering::AFace => (&ORTHO_GENERATORS[i], &ORTHO_A_VSPU[i]),
            Centering::BFace => (&ORTHO_GENERATORS[i], &ORTHO_B_VSPU[i]),
            Centering::CFace => (&ORTHO_GENERATORS[i], &ORTHO_C_VSPU[i]),
            _ => continue,
        };

        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            centering,
            generators,
            vspu,
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_monocli(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    centering: Centering,
    symprec: f64,
) -> bool {
    for i in 0..9 {
        let (generators, vspu) = match centering {
            Centering::Primitive => (&MONOCLI_GENERATORS[i], &MONOCLI_VSPU[i]),
            Centering::AFace => (&MONOCLI_GENERATORS[i], &MONOCLI_A_VSPU[i]),
            Centering::BFace => (&MONOCLI_GENERATORS[i], &MONOCLI_B_VSPU[i]),
            Centering::CFace => (&MONOCLI_GENERATORS[i], &MONOCLI_C_VSPU[i]),
            Centering::Body => (&MONOCLI_GENERATORS[i], &MONOCLI_I_VSPU[i]),
            _ => continue,
        };

        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            centering,
            generators,
            vspu,
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol_tricli(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    for i in 0..2 {
        if is_hall_symbol(
            shift,
            hall_number,
            primitive_lattice,
            symmetry,
            Centering::Primitive,
            &TRICLI_GENERATORS[i],
            &TRICLI_VSPU[i],
            symprec,
        ) {
            return true;
        }
    }
    false
}

fn is_hall_symbol(
    shift: &mut Vec3,
    hall_number: i32,
    primitive_lattice: &Mat3,
    symmetry: &Symmetry,
    centering: Centering,
    generators: &[[i32; 9]; 3],
    vspu: &[[f64; 9]; 3],
    _symprec: f64,
) -> bool {
    let (op_count, _op_start) = spgdb_get_operation_index(hall_number as usize);
    if op_count == 0 {
        return false;
    }

    let op_count_i32 = op_count as i32;
    if op_count != symmetry.size {
        return false;
    }

    // DEBUG: trace for hall 497 (Pm-3m)
    let trace = hall_number == 497;
    if trace { eprintln!("    is_hall_symbol(hall={}): op_count={}, symmetry.size={}", hall_number, op_count_i32, symmetry.size); }

    let mut rot = [[[0; 3]; 3]; 3];
    rot = unpack_generators(generators);
    if trace { eprintln!("    is_hall_symbol: generators unpacked, rot[0]={:?}, rot[1]={:?}, rot[2]={:?}", rot[0], rot[1], rot[2]); }

    let mut trans = [[0.0; 3]; 3];
    if !get_translations(&mut trans, symmetry, &rot) {
        if trace { eprintln!("    is_hall_symbol: get_translations failed"); }
        return false;
    }
    if trace { eprintln!("    is_hall_symbol: trans = {:?}", trans); }

    if get_origin_shift(shift, hall_number, &rot, &trans, centering, vspu) {
        if trace { eprintln!("    is_hall_symbol: get_origin_shift succeeded, shift={:?}", shift); }
        if is_match_database(
            hall_number,
            shift,
            primitive_lattice,
            centering,
            symmetry,
            _symprec,
        ) {
            if trace { eprintln!("    is_hall_symbol: is_match_database succeeded!"); }
            return true;
        } else {
            if trace { eprintln!("    is_hall_symbol: is_match_database failed"); }
        }
    } else {
        if trace { eprintln!("    is_hall_symbol: get_origin_shift failed"); }
    }

    false
}

/// 从扁平生成元数组解包为 3×3×3 旋转矩阵数组。
fn unpack_generators(generators: &[[i32; 9]; 3]) -> [[[i32; 3]; 3]; 3] {
    let mut rot = [[[0; 3]; 3]; 3];
    for i in 0..3 {
        for j in 0..3 {
            for k in 0..3 {
                rot[i][j][k] = generators[i][j * 3 + k];
            }
        }
    }
    rot
}

fn get_translations(
    trans: &mut [[f64; 3]; 3],
    symmetry: &Symmetry,
    rot: &[[[i32; 3]; 3]; 3],
) -> bool {
    let zero = [[0; 3]; 3];
    for i in 0..3 {
        trans[i] = [0.0; 3];
    }

    for i in 0..3 {
        if mat_check_identity_matrix_i3(&rot[i], &zero) {
            continue;
        }
        let mut is_found = false;
        for j in 0..symmetry.size {
            if mat_check_identity_matrix_i3(&symmetry.rot[j], &rot[i]) {
                trans[i] = symmetry.trans[j];
                is_found = true;
                break;
            }
        }
        if !is_found {
            return false;
        }
    }
    true
}

fn get_origin_shift(
    shift: &mut Vec3,
    hall_number: i32,
    rot: &[[[i32; 3]; 3]; 3],
    trans: &[[f64; 3]; 3],
    centering: Centering,
    vspu: &[[f64; 9]; 3],
) -> bool {
    // FIX: Handle Option return
    let (count, start_index) = spgdb_get_operation_index(hall_number as usize);
    if count == 0 {
        return false;
    }

    let mut dw = [0.0; 9];

    for i in 0..3 {
        if mat_get_determinant_i3(&rot[i]) == 0 {
            for j in 0..3 {
                dw[i * 3 + j] = 0.0;
            }
        } else {
            let mut tmp_dw = [0.0; 3];
            if set_dw(
                &mut tmp_dw,
                count,
                start_index,
                &rot[i],
                &trans[i],
                centering,
            ) {
                dw[i * 3] = mat_dmod1(tmp_dw[0]);
                dw[i * 3 + 1] = mat_dmod1(tmp_dw[1]);
                dw[i * 3 + 2] = if hall_number > 0 {
                    mat_dmod1(tmp_dw[2])
                } else {
                    tmp_dw[2]
                };
            } else {
                return false;
            }
        }
    }

    for i in 0..3 {
        shift[i] = 0.0;
        for j in 0..9 {
            shift[i] += vspu[i][j] * dw[j];
        }
    }

    shift[0] = mat_dmod1(shift[0]);
    shift[1] = mat_dmod1(shift[1]);
    shift[2] = if hall_number > 0 {
        mat_dmod1(shift[2])
    } else {
        shift[2]
    };

    true
}

fn set_dw(
    dw: &mut Vec3,
    count: usize,
    start_index: usize,
    rot: &Mat3I,
    trans: &Vec3,
    centering: Centering,
) -> bool {
    let mut trans_prim = [0.0; 3];
    trans_prim = transform_translation(centering, trans);

    for i in 0..count {
        if let Some((rot_db, trans_db)) = spgdb_get_operation_by_index(start_index + i) {
            let mut trans_db_prim = [0.0; 3];
            trans_db_prim = transform_translation(centering, &trans_db);

            if mat_check_identity_matrix_i3(&rot_db, rot) {
                for j in 0..3 {
                    dw[j] = trans_prim[j] - trans_db_prim[j];
                }
                return true;
            }
        }
    }
    false
}

/// 将分数平移变换到约化原胞表示。
fn transform_translation(centering: Centering, trans: &Vec3) -> Vec3 {
    match centering {
        Centering::Primitive => *trans,
        Centering::Body => mat_multiply_matrix_vector_id3(&M_BCC, trans),
        Centering::Face => mat_multiply_matrix_vector_id3(&M_FCC, trans),
        Centering::AFace => mat_multiply_matrix_vector_id3(&M_AC, trans),
        Centering::BFace => mat_multiply_matrix_vector_id3(&M_BC, trans),
        Centering::CFace => mat_multiply_matrix_vector_id3(&M_CC, trans),
        Centering::RCenter => mat_multiply_matrix_vector_id3(&M_RC, trans),
        _ => *trans,
    }
}

/// 将旋转矩阵变换到约化原胞表示 (cartesian)。
fn transform_rotation(centering: Centering, rot: &Mat3I) -> Mat3 {
    let rot_d3 = mat_cast_matrix_3i_to_3d(rot);

    if centering != Centering::Primitive {
        let inv_matrix = match centering {
            Centering::Body => Some(&M_BCC_INV),
            Centering::Face => Some(&M_FCC_INV),
            Centering::AFace => Some(&M_AC_INV),
            Centering::BFace => Some(&M_BC_INV),
            Centering::CFace => Some(&M_CC_INV),
            Centering::RCenter => Some(&M_RC_INV),
            _ => None,
        };

        if let Some(m_inv) = inv_matrix {
            if let Ok(res) = mat_get_similar_matrix_d3(&rot_d3, m_inv, 0.0) {
                return res;
            }
        }
    }
    rot_d3
}

fn is_match_database(
    hall_number: i32,
    origin_shift: &Vec3,
    primitive_lattice: &Mat3,
    centering: Centering,
    symmetry: &Symmetry,
    symprec: f64,
) -> bool {
    // FIX: Handle Option return
    let (count, start_index) = spgdb_get_operation_index(hall_number as usize);
    if count == 0 {
        return false;
    }

    let mut found_list = vec![false; count];
    let aperiodic = AperiodicAxis::Z;

    for i in 0..symmetry.size {
        let mut is_found = false;
        for j in 0..count {
            // FIX: Handle Option return
            if let Some((rot_db, trans_db)) = spgdb_get_operation_by_index(start_index + j) {
                if mat_check_identity_matrix_i3(&symmetry.rot[i], &rot_db) {
                    let mut trans_db_prim = [0.0; 3];
                    trans_db_prim = transform_translation(centering, &trans_db);

                    let mut trans_prim = [0.0; 3];
                    trans_prim = transform_translation(centering, &symmetry.trans[i]);

                    let mut rot_prim = [[0.0; 3]; 3];
                    rot_prim = transform_rotation(centering, &rot_db);

                    let mut diff = [0.0; 3];
                    for k in 0..3 {
                        diff[k] = trans_prim[k] - trans_db_prim[k] + origin_shift[k];
                    }

                    let shift_rot = mat_multiply_matrix_vector_d3(&rot_prim, origin_shift);

                    let overlap = if hall_number > 0 {
                        cel_is_overlap(&diff, &shift_rot, primitive_lattice, symprec)
                    } else {
                        cel_layer_is_overlap(
                            &diff,
                            &shift_rot,
                            primitive_lattice,
                            aperiodic,
                            symprec,
                        )
                    };

                    if overlap {
                        if !found_list[j] {
                            found_list[j] = true;
                            is_found = true;
                            break;
                        }
                    }
                }
            }
        }

        if !is_found {
            return false;
        }
    }

    true
}