Sólidos arquimedianos: aplicações com dobraduras

Abstract

This work seeks to present in a general way the Archimedean solids. To do so, topics such as Plato's polyhedra and their relationships with the Archimedeans will be addressed. We will present the 13 Archimedes solids and observe the non-existence of others. We noticed that in High School the Platonic solids are approached, but little is said about the existence of Archimedes. The form used for such a presentation, in addition to the theoretical part and in line with the skills and competences suggested by the National Common Curricular Base (BNCC), will be the construction of the truncated icosahedron through folding. We will therefore address the concept of folding and the necessary axioms for its implementation. We will also talk about some necessary constructions of plane geometry, such as the equilateral triangle, the barycenter and the regular hexagon. The objective of the research is to make students recognize such solids and, in a playful way, manage to make them using folding, above all realizing the mathematical development that is behind the activity.