18 Oct '09 04:02

As many wargamers know, you cannot fill up a flat surface with any regular polygon with more than six sides. Hexes work; squares work; triangles work. I'm not sure about pentagons, but septagons, octagons etc do NOT work.

Can this sort of thought be extended to three dimensions? What are the three dimensional versions of regular polygons? Are they the Platonic Solids? If so, why are there only five of the latter, but infinitely many of the former?

Can this sort of thought be extended to three dimensions? What are the three dimensional versions of regular polygons? Are they the Platonic Solids? If so, why are there only five of the latter, but infinitely many of the former?