Tuesday, March 22, 2016

[twcnbxba] Cube with colored faces

There are 30 ways to color the faces a cube with 6 given distinct colors.  One of them is the canonical Rubik's cube coloring.  (Previously, allowing color permutation.)

Assemble a full set of 1x1x1 Rubik's cubes with all the possible colorings.  2x3x5 cuboid.

The 30 cubes could be a 30 letter 3-dimensional alphabet.  It is truly 3-dimensional: a single photograph of a letter cube, being able to see at most 3 sides, is ambiguous.  Each cube can be oriented 24 different ways = 720.

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