Question: Does there exist a subset S E 3 such that its group of isometries S has only 4 fixed points: (0 , 0 , 0)

Does there exist a subset S E3 such that its group of isometries S has only 4 fixed points:

(0, 0, 0),(1, 0, 0),(0, 1, 0),(0, 0, 1)? If, yes, provide an example. If not, explain why it does not exist.

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