Recently started getting back into modular nonsense. In an art trade, I got a modular Infinitaur, which got me to thinking.

He's always had the floating eyes, which isn't modular per se, they're connected to him, just out of sight. It turns out that since he lives in higher dimensions, he can APPEAR to be any form of modular by embedding himself just right in 3d space. So that means while in reality he can't detach parts of himself, he can sure create the illusion!

In addition, this answers the question of what happens when he gets tangled up. He simply phases the tangled part of him into higher dimensions which aren't limited by 3d, untangles there, then re-embeds. All without having to thread any needles. :D

It's been a while since I took topology but all this seems reasonable mathematically. I leave the proofs as an exercise to the reader. :P
This also reminds me that it's high time to make the annual Infinitaur comic...