Hole Punch

positions = [0, 1, 2, 5, 6, 7, 10, 11, 12]
rotations = [
    [0, 1, 2, 3, 4, 5, 6, 7, 8],
    [2, 5, 8, 1, 4, 7, 0, 3, 6],
    [8, 7, 6, 5, 4, 3, 2, 1, 0],
    [6, 3, 0, 7, 4, 1, 8, 5, 2],
]

shapes = set()
for n in range(1, 2**9):
    rotated = []
    for rot in rotations:
        shape = 0
        for bit, pos in zip(rot, positions):
            if n & (1 << bit):
                shape += 1 << pos

        while shape and not (shape & 1):
            shape >>= 1
        rotated.append(shape)

    shapes.add(min(rotated))

for shape in sorted(shapes):
    print bin(shape)

print len(shapes)