Poliedros arquimedianos

Abstract

The subject of this dissertation is Archimedean (or semi-regular) polyhedra, solid that are obtained through operations (truncation and snub ) made on regular convex polyhedra. As far as we know, such polyhedra were studied by Archimedes over 2000 years ago, but it was the German astronomer and mathematician Johann Kepler who named them and proved the existence of only 13 (thirteen), except for a class of prisms and anti-prisms. Our main objective is to propose a complete theoretical material on the Archimedean polyhedron theory so that it can be used by high school mathematics teachers as well as for undergraduate students in Mathematics, as well as to present some results obtained through an implementation of a workshop on this topic. From the results obtained in the practical part of the workshop, mainly, we believe that this theme, quite playful, besides stimulating the imagination and the creativity of the students, can really be introduced from high school, through examples and exercises similar to those that will be proposed in this work. In this work we will also show how to construct some polyhedra with the use of Sagemath, a program of free (and open source) software, specially designed to work in the area of Mathematics.