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Title: A new class of monohedral pentagonal spherical tilingswith GeoGebra
Author: Breda, Ana
Santos, José M. Santos dos
Keywords: Spherical geometry
Spherical tilings
Issue Date: Feb-2018
Publisher: European Mathematical Society
Abstract: By a monohedral spherical tiling we mean a decomposition of the sphereby geodesic congruent polygons. Here, making use of GeoGebra, a well known freeinteractive mathematics software, we show how to generate new classes of monohedralnon-convex triangular and new non-convex pentagonal spherical tilings, changing theside gluing rules of the regular spherical tetrahedral tiling, by means of a local actionof particular subgroups of spherical isometries. In both cases each face haspas areameasure.In relation to the new class of pentagonal tilings, we describe some of their propertiesand show the existence, in a special case, of an associated dihedral triangular spherical til-ing, that is, a tiling composed by two sets of congruent triangles.These classes of spherical tilings have emerged as a result of an interative constructionprocess, only possible by the use of newly produced GeoGebra tools and the dynamic inter-action capabilities of this software.
Peer review: yes
DOI: 10.4171/PM/2006
ISSN: 0032-5155
Appears in Collections:CIDMA - Artigos
AGG - Artigos

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