Is it possible to choose a set of
![100](/media/m/c/c/c/ccc0563efabf7c1a3d81b0dc63f5b627.png)
(or
![200](/media/m/d/b/1/db17fa4815fe209746e70206b8e27264.png)
) points on the boundary of a cube such that this set is fixed under each isometry of the cube into itself? Justify your answer.
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Is it possible to choose a set of $100$ (or $200$) points on the boundary of a cube such that this set is fixed under each isometry of the cube into itself? Justify your answer.