Dihedral F-tilings of the sphere by equilateral and scalene triangles. I.
type: Item
instance of: scholarly article
title: Dihedral F-tilings of the sphere by equilateral and scalene triangles. I.
zbMATH Open document ID: 1211.52021
DOI: 10.4171/RSMUP/124-1
author: Patrícia S. Ribeiro
author: Ana M. R. Azevedo Breda
author: Altino Manuel Folgado dos Santos
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2011-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/241282
full work available at URL: http://rendiconti.math.unipd.it/volumes/vol124.php
review text: A polygonal tiling of the Euclidean sphere \(S^2\), where the edges of the polygon are geodesics, is called an \(f\)-tiling if all vertices are of even valency and the sums of alternate angles around each vertex is \(\pi\). The tiling is called dihedral if each prototile is congruent to one of two fixed figures. The authors show that a dihedral \(f\)-tiling of the sphere with an equilateral spherical triangle and a scalene spherical triangle such that the long side of the scalene triangles are adjacent to the equilateral triangles belongs to one of two families, which they explicitly describe. The proof follows a case by case analysis, considering the placement of the first few tiles.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 20B35
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 5849492
zbMATH Keywords: spherical tiling
zbMATH Keywords: dihedral tiling
reviewed by: Ali Ulas Özgür Kisisel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5849492