JournalspmVol. 74, No. 3pp. 257–266

A new class of monohedral pentagonal spherical tilings with GeoGebra

  • Ana M. d'Azevedo Breda

    Universidade de Aveiro, Portugal
  • José M. Dos Santos Dos Santos

    Universidade Aberta, Lisboa, Portugal
A new class of monohedral pentagonal spherical tilings with GeoGebra cover
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Abstract

By a monohedral spherical tiling we mean a decomposition of the sphere by geodesic congruent polygons. Here, making use of GeoGebra, a well known free interactive mathematics software, we show how to generate new classes of monohedral non-convex triangular and new non-convex pentagonal spherical tilings, changing the side gluing rules of the regular spherical tetrahedral tiling, by means of a local action of particular subgroups of spherical isometries. In both cases each face has π\pi as area measure.

In relation to the new class of pentagonal tilings, we describe some of their properties and show the existence, in a special case, of an associated dihedral triangular spherical tiling, that is, a tiling composed by two sets of congruent triangles. These classes of spherical tilings have emerged as a result of an interative construction process, only possible by the use of newly produced GeoGebra tools and the dynamic interaction capabilities of this software.

Cite this article

Ana M. d'Azevedo Breda, José M. Dos Santos Dos Santos, A new class of monohedral pentagonal spherical tilings with GeoGebra. Port. Math. 74 (2017), no. 3, pp. 257–266

DOI 10.4171/PM/2006