Poliedros de kepler-Poinsot: explorando poliedros regulares não convexos com o geogebra
Visualizar/ Abrir
Data
2022-02-01Autor
http://lattes.cnpq.br/5466673923692736
ARAGÃO, Fabrícia Pinho
Metadata
Mostrar registro completoResumo
This work deals with regular non-convex polyhedra, known as Kepler-Poinsot polyhedra. Its
general objective is to use dynamic geometry resources to expand the understanding about the
following questions: why are Kepler-Poinsot polyhedra considered regular polyhedra? What
are the vertices, edges and faces of these polyhedra? Although these questions may seem
obvious, answering them requires diving into another question: what, in fact, is a polyhedra?
During the development of the work, we showed that there is more than one way to define what
a polyhedron is and we sought, with the help of the Geogebra software, to make it clear which
polygons should be understood as faces of Kepler-Poinsot polyhedra so that they can be
interpreted as regular polyhedra. Considering the different possibilities in choosing a definition
of a polyhedron suitable for our purposes, we opted for the one proposed by Branko Grünbaum
(2003), which differentiates the combinatorial structure of a polyhedron from its geometric
interpretation, allowing a more general understanding of the structures we call a polyhedra.
According to the definition we chose, a face is understood as a circuit composed of vertices and
edges, in such a way that the faces that constitute the Kepler-Poinsot polyhedra can be
interpreted as intersecting regular polygons. Answering all these questions requires a lot of
abstract thinking, which justifies the use of dynamic geometry as a visual support in order to
facilitate the path that leads to such abstractions. Thus, the exposition made throughout this
work makes use of constructions produced by the author and made available on the Geogebra
online platform to make these ideas clearer, thus achieving the proposed objectives.