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Is it possible for a non-co-planar set of points to be symmetric about a point but not symmetric about a plane?

I am pretty sure this is true but I can't think of an example.

Things that I think don't work:

  • Sphere
  • Cone
  • Pyramid
  • Cube
  • Prisms
  • cylinder
  • hedrons (tetrahedron, dodecahedron, polyhedron, etc.)
Zachooz
  • 169
  • 7

2 Answers2

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Consider a letter $F$ in the plane $x=1$ and its reflection through the origin.

enter image description here

Robert Israel
  • 448,999
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Yes. It is not possible because a non-co-planar set of points to be symmetric about a point but not symmetric about a plane is not possible in your situation.