Platonic solid

(geometry Plato) - polyhedron satisfying the following three conditions: well formed Platonic polyhedra ar e a special case półforemnych (archimedesowskich), in which wel l formed walls need not be identical (congruent tj.wzajemnie). Th ere are five regular polyhedra (up to similarity)): The first evidence is based on an analysis of the total volume of the internal angles of the walls coincide with any vertex. A second less elementary proof relies on Eulers theorem on polyhedra: where W is the number of vertices of a polyhedron, S the number of its walls, and K the number of edges.