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Stimulated by the last thread, where the representations of permutations and orientations was dealt I want to ask, what would be a good representation for the 12! edge permutations on the coordinate level, if the right multiplication of the edge permutation by any of the generators U,L.... should also be done with a MoveTable on the coordinate level like newcoordinate = MoveTable[oldcoodinate][generator].

This MoveTable would have 12!*18 4 Byte entries when we take the coordinate from 0..12!-1 and of course is far too big. Of course we could reduce this by 48 symmetries, but then we still would have a very large table.