definition of the Cross Teaser group

crossteaser.py

'''
definition of the Cross Teaser group, using my groups library:
<https://github.com/mildsunrise/finite-algebra>

the puzzle is tilted 45 degrees, with the front slots in *down right* direction.
crosses are assigned in clockwise order, starting from the upper cross:

    0
  7   1
6   .   2
  5   3
    4

each of the CubeRot axis rotations cause the top face to move in these directions:

    Z (clockwise turn)
    o
  .   .
Y       X

consult <https://tech.lgbt/@mildsunrise/110286601977677670> for more detailed info.
'''

from groups import WreathProduct, S8, CubeRot

X, Y, Z = CubeRot.X, CubeRot.Y, CubeRot.Z
Xp, Yp, Zp = CubeRot.Xp, CubeRot.Yp, CubeRot.Zp
X2, Y2, Z2 = CubeRot.X2, CubeRot.Y2, CubeRot.Z2

class CrossTeaser(WreathProduct):
	BOTTOM = CubeRot
	TOP = S8

# we can embed the klein four-group (symmetries of a non-square rectangle) in this group
ROT180 = CrossTeaser((Z2,) * 8, S8.FULL_CYCLE ** 4)
FLIPH = CrossTeaser((Zp * Y2,) * 8, S8.REVERSED * S8.FULL_CYCLE.inv)
FLIPV = FLIPH * ROT180

# clockwise cycle of the Upper and Right 3 crosses
U = CrossTeaser.from_cycles(( [7,0,1], [Y, X, Xp*Yp] ))
R = CrossTeaser.from_cycles(( [1,2,3], [X, Yp, Y*Xp] ))
# derive other 2 base moves
D, L = map(ROT180.conj, (U, R))