Euler characteristic and Platonic solids -- Stanislav Jabuka, April 20, 2004

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We'll start by defining the Euler characteristic for 
triangulated polygons and check that it is independent 
of the particular triangularization chosen. 


As an application of the Euler characteristic we'll 
see that one can readily obtain a complete list of the 
Platonic solids. A Platonic solid is a polyhedra whose 
boundary is a polygon all of whose sides are regular n-gons 
and all of whose vertices have the same valence. This 
list was already known in the times of Plato et al.