reid_tiling():
  python version: 3.8.10
  numpy version:  1.24.2
  reid_tiling() uses the RREF to uncover tilings of the Reid polygon.


  Shape of the Reid polygon:

[[1. 1. 0.]
 [1. 1. 1.]
 [1. 1. 1.]]

  Tile 0:

[1. 1.]

  The matrix A:


  The RREF of A+b

[[ 1.  0.  0.  0.  0.  0.  1.  0. -1.  0.  0.]
 [ 0.  1.  0.  0.  0.  0.  0.  0.  1.  0.  1.]
 [ 0.  0.  1.  0.  0.  0.  1.  0. -1.  0.  0.]
 [ 0.  0.  0.  1.  0.  0.  0.  0.  1.  1.  1.]
 [ 0.  0.  0.  0.  1.  0.  0.  0.  0.  1.  1.]
 [ 0.  0.  0.  0.  0.  1. -1.  0.  1.  0.  1.]
 [-0. -0. -0. -0. -0. -0. -0.  1. -0. -1. -0.]
 [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]]

  The new linear system C:

[[ 1.  0.  0.  0.  0.  0.  1.  0. -1.  0.]
 [ 0.  1.  0.  0.  0.  0.  0.  0.  1.  0.]
 [ 0.  0.  1.  0.  0.  0.  1.  0. -1.  0.]
 [ 0.  0.  0.  1.  0.  0.  0.  0.  1.  1.]
 [ 0.  0.  0.  0.  1.  0.  0.  0.  0.  1.]
 [ 0.  0.  0.  0.  0.  1. -1.  0.  1.  0.]
 [ 0.  0.  0.  0.  0.  0.  1.  0.  0.  0.]
 [-0. -0. -0. -0. -0. -0. -0.  1. -0. -1.]
 [ 0.  0.  0.  0.  0.  0.  0.  0.  1.  0.]
 [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  1.]]

  The free variable indices f:

[6 8 9]

  Legal solutions:

[0. 1. 0. 1. 1. 1. 0. 0. 0. 0.]
[1. 0. 1. 0. 1. 0. 0. 0. 1. 0.]
[0. 1. 0. 0. 0. 1. 0. 1. 0. 1.]
[0. 0. 0. 0. 1. 1. 1. 0. 1. 0.]