Different Possible Configurations of the MF8 Crazy Doderhombus

configurations.txt

143 configurations other than all ones
Numbers correspond to the faces in this order:
white, pink, yellow, tan, green, light blue, light green, blue, orange, purple, gray, red
default: (1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1)
(0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0)
(0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1)
(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
(0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0)
(0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0)
(0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0)
(0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1)
(0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1)
(0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1)
(0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1)
(0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0)
(0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1)
(0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0)
(0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1)
(0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1)
(0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1)
(0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1)
(0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1)
(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0)
(0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1)
(0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1)
(0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1)
(0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1)
(0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0)
(0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1)
(0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0)
(0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0)
(0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1)
(0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1)
(0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0)
(0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1)
(0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1)
(0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0)
(0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0)
(0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1)
(0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1)
(0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1)
(0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0)
(0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1)
(0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0)
(0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0)
(0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0)
(0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0)
(0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0)
(0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0)
(0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0)
(0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0)
(0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1)
(0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1)
(0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0)
(0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1)
(0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1)
(0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1)
(0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0)
(0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1)
(0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1)
(0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0)

crazy_doderhombus_configurations.py

import itertools

# Here's the color scheme on my puzzle:
# Facing a 4-sided corner, starting with a side up, going clockwise
# white, pink, yellow, tan,
# Then going clockwise around the middle layer,
# dark green is next to white and pink, then light blue, light green, dark blue,
# then going around the back clockwise (without reorienting),
# orange is next to dark blue and dark green, then purple, gray, and red.
# Number them like this:
# 0: white
# 1: pink
# 2: yellow
# 3: tan
# 4: green
# 5: light blue
# 6: light green
# 7: blue
# 8: orange
# 9: purple
# 10: gray
# 11: red

names = ['white', 'pink', 'yellow', 'tan', 'green', 'light blue',
         'light green', 'blue', 'orange', 'purple', 'gray', 'red']

reflection = [0, 3, 2, 1, 7, 6, 5, 4, 8, 11, 10, 9]
rot0 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
rot1 = [1, 2, 3, 0, 5, 6, 7, 4, 9, 10, 11, 8]
rot2 = [2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9]
rot3 = [3, 0, 1, 2, 7, 4, 5, 6, 11, 8, 9, 10]
rot4 = [4, 9, 5, 1, 8, 10, 2, 0, 7, 11, 6, 3]
rot5 = [5, 10, 6, 2, 9, 11, 3, 1, 4, 8, 7, 0]
rot6 = [6, 11, 7, 3, 10, 8, 0, 2, 5, 9, 4, 1]
rot7 = [7, 8, 4, 0, 11, 9, 1, 3, 6, 10, 5, 2]
rot8 = [8, 11, 10, 9, 7, 6, 5, 4, 0, 3, 2, 1]
rot9 = [9, 8, 11, 10, 4, 7, 6, 5, 1, 0, 3, 2]
rot10 = [10, 9, 8, 11, 5, 4, 7, 6, 2, 1, 0, 3]
rot11 = [11, 10, 9, 8, 6, 5, 4, 7, 3, 2, 1, 0]


rotations = [rot0, rot1, rot2, rot3, rot4, rot5,
             rot6, rot7, rot8, rot9, rot10, rot11]

def compose_permutations(p1, p2):
    assert len(set(p1)) == len(p1)
    assert len(set(p2)) == len(p2)
    return [p2[ix] for ix in p1]

# Add in rotating the face in position 0 180 degrees.
rot_face = [0, 7, 8, 4, 3, 11, 9, 1, 2, 6, 10, 5]
rotations = rotations + [compose_permutations(rot_face, rot) for rot in rotations]

reflected_rotations = [compose_permutations(rot, reflection) for rot in rotations]

equivalences = rotations + reflected_rotations

# Now get the puzzle variants that aren't equivalent
# under rotation/reflection

# Make sure the default is in the list and not its mirror image.
default = (1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1)

configurations = {default}

for config in itertools.product([0, 1], repeat=12):
    equivalent_configs = [tuple([config[ix] for ix in equiv]) for equiv in equivalences]
    for equiv in equivalent_configs:
        if equiv in configurations:
            break
    else:
        configurations.add(tuple(config))

# Remove the all ones configuration since
# that's equivalent to a standard doderhombus.
configurations.remove((1,) * 12)

print(len(configurations), "configurations other than all ones")
print("Numbers correspond to the faces in this order:")
print("white, pink, yellow, tan, green, light blue, light green, blue, orange, purple, gray, red")
print("default:", default)
for config in configurations:
    if config != default:
        print(config)