pack 0.1.0

Solver for a packing puzzle.
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# Packing Puzzle
Solver for a packing puzzle.

## Symmetries
The group of symmetries of the cube is isomorphic to the permutation group on 4
symbols. Below is an explicit isomorphism between S4 and a matrix group.

| Permutation |  x |  y |  z | matrix                                             | 
|-------------|----|----|----|----------------------------------------------------|
| 0123        |  x |  y |  z | [ [  1,  0,  0 ], [  0,  1,  0 ], [  0,  0,  1 ] ] |
| 0132        | -z | -y | -x | [ [  0,  0, -1 ], [  0, -1,  0 ], [ -1,  0,  0 ] ] |
| 0213        | -x | -z | -y | [ [ -1,  0,  0 ], [  0,  0, -1 ], [  0, -1,  0 ] ] |
| 0231        |  y |  z |  x | [ [  0,  1,  0 ], [  0,  0,  1 ], [  1,  0,  0 ] ] |
| 0312        |  z |  x |  y | [ [  0,  0,  1 ], [  1,  0,  0 ], [  0,  1,  0 ] ] |
| 0321        | -y | -x | -z | [ [  0, -1,  0 ], [ -1,  0,  0 ], [  0,  0, -1 ] ] |
| 1023        |  z | -y |  x | [ [  0,  0,  1 ], [  0, -1,  0 ], [  1,  0,  0 ] ] |
| 1032        | -x |  y | -z | [ [ -1,  0,  0 ], [  0,  1,  0 ], [  0,  0, -1 ] ] |
| 1203        | -z | -x |  y | [ [  0,  0, -1 ], [ -1,  0,  0 ], [  0,  1,  0 ] ] |
| 1230        | -y |  x |  z | [ [  0, -1,  0 ], [  1,  0,  0 ], [  0,  0,  1 ] ] |
| 1302        |  x |  z | -y | [ [  1,  0,  0 ], [  0,  0,  1 ], [  0, -1,  0 ] ] |
| 1320        |  y | -z | -x | [ [  0,  1,  0 ], [  0,  0, -1 ], [ -1,  0,  0 ] ] |
| 2013        | -y |  z | -x | [ [  0, -1,  0 ], [  0,  0,  1 ], [ -1,  0,  0 ] ] |
| 2031        |  x | -z |  y | [ [  1,  0,  0 ], [  0,  0, -1 ], [  0,  1,  0 ] ] |
| 2103        |  y |  x | -z | [ [  0,  1,  0 ], [  1,  0,  0 ], [  0,  0, -1 ] ] |
| 2130        |  z | -x | -y | [ [  0,  0,  1 ], [ -1,  0,  0 ], [  0, -1,  0 ] ] |
| 2301        | -x | -y |  z | [ [ -1,  0,  0 ], [  0, -1,  0 ], [  0,  0,  1 ] ] |
| 2310        | -z |  y |  x | [ [  0,  0, -1 ], [  0,  1,  0 ], [  1,  0,  0 ] ] |
| 3012        |  y | -x |  z | [ [  0,  1,  0 ], [ -1,  0,  0 ], [  0,  0,  1 ] ] |
| 3021        | -z |  x | -y | [ [  0,  0, -1 ], [  1,  0,  0 ], [  0, -1,  0 ] ] |
| 3102        | -y | -z |  x | [ [  0, -1,  0 ], [  0,  0, -1 ], [  1,  0,  0 ] ] |
| 3120        | -x |  z |  y | [ [ -1,  0,  0 ], [  0,  0,  1 ], [  0,  1,  0 ] ] |
| 3201        |  z |  y | -x | [ [  0,  0,  1 ], [  0,  1,  0 ], [ -1,  0,  0 ] ] |
| 3210        |  x | -y | -z | [ [  1,  0,  0 ], [  0, -1,  0 ], [  0,  0, -1 ] ] |