Edging out a coloring

Discrete Mathematics Level pending

A cube has vertices \(ABCDEFGH.\) The 12 edges of the cube are each coloured one of four colours subject to the following conditions:

A) Each colour appears exactly once around each face of the cube.

B) No two faces of the cube have the same cyclic ordering of the colors (taken clockwise).

How many different ways are there to colour the edges of the cube?


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