How to calculate all 24 rotations of 3d array?

Look at the code for rot90. I see 3 variations on flip and swapaxes, depending on k the axis parameter.

fliplr(m).swapaxes(0, 1)
fliplr(flipud(m))
fliplr(m.swapaxes(0, 1))

fliplr(m) is just m[:, ::-1], and not surprisingly, flipud is m[::-1, ...].

You could flip the 3rd axis with m[:,:,::-1], or m[...,::-1].

np.transpose is another tool for permuting axes, that may, or may not, be easier to use than swapaxes.

If rot90 gives you 4 of the rotations, you should be able apply the same routines to produce the others. You just have to understand the logic underlying rot90.

e.g.

def flipbf(m):
    return m[:,:,::-1]

flipbf(m).swapaxes(0, 2)
flipbf(m).swapaxes(1, 2)
etc

Update: Simplified after 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