How to calculate all 24 rotations of 3d array?

Question

I have a 3d numpy array describing a polycube (imagine a 3d tetris piece). How can I calculate all 24 rotations?

Numpy\'s array manipulation routines includes a rot90 me

Answer 1

Update: Numpy 1.12.0 added an axes argument to the rot90 function

Here's how I made all 24 rotations:

from numpy import rot90, array

def rotations24(polycube):
    """List all 24 rotations of the given 3d array"""
    def rotations4(polycube, axes):
        """List the four rotations of the given 3d array in the plane spanned by the given axes."""
        for i in range(4):
             yield rot90(polycube, i, axes)

    # imagine shape is pointing in axis 0 (up)

    # 4 rotations about axis 0
    yield from rotations4(polycube, (1,2))

    # rotate 180 about axis 1, now shape is pointing down in axis 0
    # 4 rotations about axis 0
    yield from rotations4(rot90(polycube, 2, axes=(0,2)), (1,2))

    # rotate 90 or 270 about axis 1, now shape is pointing in axis 2
    # 8 rotations about axis 2
    yield from rotations4(rot90(polycube, axes=(0,2)), (0,1))
    yield from rotations4(rot90(polycube, -1, axes=(0,2)), (0,1))

    # rotate about axis 2, now shape is pointing in axis 1
    # 8 rotations about axis 1
    yield from rotations4(rot90(polycube, axes=(0,1)), (0,2))
    yield from rotations4(rot90(polycube, -1, axes=(0,1)), (0,2))

Test that all 24 rotations are indeed distinct:

polycube = array([[[1, 1, 0],
        [1, 1, 0],
        [0, 0, 0]],

       [[0, 0, 0],
        [1, 0, 0],
        [1, 0, 0]],

       [[0, 0, 0],
        [0, 0, 0],
        [0, 0, 0]]])

assert len(set(str(x) for x in rotations24(polycube))) == 24