Exercise 2.1.10 (Isometry Cube)

Question

Example 	extbf{2.1.9(iii)} shows that the action of the isometry
group $G$ of the cube on the set $X$ of long diagonals is not faithful.
By 	extbf{Lemma 2.1.8}, there must be some non-identity isometry of the
cube that fixes all four long diagonals. In fact, there is exactly one.
What is it?

Richard Ganaye · Accepted Answer

The symmetry $s_0$ relative to the center $O$ of the cube preserves each of the four long diagonals, and is a non-identity isometry.

Exercise 2.1.10 (Isometry Cube)

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Exercise 2.1.10 (Isometry Cube)

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