Octahedron is bullshit. One of these days we're going to find out that doesn't actually work
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in reply to @sedge's post:
okay, this one is true, right? like those two shapes are the complements of each other or whatever that's called?
I think of them more as tetrahedrons with corners sanded down until the sanded spots meet at points.
Incidentally, if you take a hypercube with all corners at (±1,±1,±1,±1), rotate it about the origin to put two of the corners at (±2,0,0,0), and then start slicing it at different w-values, you see this tetrahedron->octahedron transformation between w=-1 and w=0.
in reply to @mousefountain's post:
I was a lot more mad at that until I read the article and found out that every face touches every face. This is the answer to a cursed problem, of course it's going to be a fucked up little demon.
it's a twisted creature, for sure, but i'd def keep a triangulated mesh version of it around to test pathological renderer cases.
this thing is incredible, i had no idea! My favorite polyhedron fact is that the infinite hexagonal plane is technically a regular polyhedron.