Oo.. I'm gonna have to read this later while I shit in the dark because my office things it's a different time.
While we're on the subject, you may not be aware of what's possibly considered the most counter intuitive "paradox" in geometry
https://en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Discussion
TLDR you can take a unit sphere, chop into 5 (I think) disjoint pieces, and reassemble them with normal 3D motions (no bending, just isometries or whatever - basically moving or twisting allowed) and get two spheres with no holes. Construction relies on controversial (but highly useful and widely accepted) axiom of choice. Pieces are "infinitely sharp" lol
My son is going to be very dissapointed with what Im about to do to one of his playballs