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Permutation Groups - Rigid Motion of a Cube

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A rigid motion of a cube can be thought of either as a permutation of its 8 vertices or as a permutation of its 6 sides. Find a rigid motion of a cube that has order 3, and express the permutation that represents it in both ways, as a permutation on 8 elements and as a permutation on 6 elements.

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Rigid motions of a cube are investigated. The solution is detailed and well presented. The solution received a rating of "5" from the student who posted the question.

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