Symmetry in Space

Question

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.)

Answer 1

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

Answer 2

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.