Característica de Euler-Poincaré para poliedros 𝑛-tóricos

Abstract

The Euler-Poincaré Characteristic is a well-known topological invariant. The computation for compact surfaces depends on a highly refined topological tools, however in the case of convex polyhedra this invariant is constant equal to two and it follows, because convex polyhedra are homeomorphic to a sphere, from a simple verification of the formula which relates the number of vertices V, the number of edges A and the number of faces F of a polyhedron, more precisely, V − A + F = 2 (Euler’s Formula). In this work we present a proof, using only finite induction, for the computation this invariant taking into account, however, only a class of non-convex polyhedra, presented in a specific way, here called n-toric polyhedra, which are homeomorphic to an n-torus.