Re: [math-fun] existence of the icosahedron

Oof. Forget I asked that... this is the proof that Coxeter gives on p.5 of _Regular Polytopes_. --Michael Kleber kleber@brandeis.edu On Tuesday, March 2, 2004, at 11:12 AM, Michael Kleber wrote:

Does anyone know the pedigree of the following line of reasoning? I haven't defined "by continuity," but I think the intent will be clear from the proof. [...] There you have it: the polyhedron so constructed clearly has twenty equilateral triangular faces meeting five at each vertex.