A cube with distinct faces can be rotated to 24 different orientations. Curiously, there are also 24 permutations of 4 objects, so 4 cubes can be in 24^5 different states, about 8 million.
Vaguely similar is the isomorphism between 60 orientations of an icosahedron and the alternating group A[5].
Update: the rotation group of a cube is isomorphic with the symmetric group of 4 objects S(4).
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