Do solids retain their symmetry after uniform truncation?

Question

I was looking at platonic solids and Archimedean solids. I observed that the point group of the solids still the same after uniform truncation. Examples of this is that Cube, truncated cube, cuboctahedron, truncated octahedron, and octahedron all have symmetry of octahedral symmetry ($O_h$).

My question is, if this worked for platonic solid, do this also true for any arbitrary solid? Or is there a condition? I mean, I don't think it worked in 2D.