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From: graner@ut-ngp.UTEXAS (Nicolas Graner)
Newsgroups: net.math
Subject: Euler's(?) formula
Message-ID: <1832@ut-ngp.UTEXAS>
Date: Sat, 15-Jun-85 14:34:23 EDT
Article-I.D.: ut-ngp.1832
Posted: Sat Jun 15 14:34:23 1985
Date-Received: Tue, 18-Jun-85 02:09:01 EDT
Distribution: net
Organization: UTexas Computation Center, Austin, Texas
Lines: 11

I think it was Euler who showed that a polyhedron with F faces,
V vertices and E edges satisfies the relation: F + V = E + 2.

I have seen a very technical proof, but the result is so simple and
beautiful that there should be a simple and beautiful proof (i.e.
accessible to non mathematicians). Does anyone know of such a proof?
Also, to what kind of polyhedrons does it apply (convex, connected...) ?

Nic.                      {ihnp4,seismo,allegra,...}!ut-ngp!graner

*If Murphy's law can go wrong, it won't*