Composite faces and their quantification for eulerian polyhedrons

Abstract

Polyhedra are three-dimensional objects consisting of polygons, such polygons are their faces. The polyhedron that is observed has visible faces and hidden faces, this object can be represented in the plane with the identification of edges of visible faces and hidden faces. After this projection, its visible or hidden edges intersect, providing perimeters of polygons that are not their faces. Soon the objectives of this work were to identify these polygons, analyzing the content already found in the geometry and under what circumstances it was possible to quantify them. The results of this work implied the denomination of polygons as Composite Faces, constructively pointed out how to generate them from the projection of a polyhedron and based on the cauchy demonstration, presented by Elon Lages Lima, it was possible to establish to the quantification of Composite Faces for Eulerian polyhedra.