JournalsrsmupVol. 124pp. 1–23

Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles-I

  • Ana M. d'Azevedo Breda

    Universidade de Aveiro, Portugal
  • Patrícia S. Ribeiro

    E.S.T. Setúbal, Setubal, Portugal
  • Altino F. Santos

    Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal
Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles-I cover
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Abstract

The study of dihedral f-tilings of the Euclidean sphere _S_2 by triangles and r-sided regular polygons was initiated in 2004 where the case r = 4 was considered [6]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and r-sided regular polygons, for any r ≥ 5, was described. Later on, in [3] the classfication of all f-tilings of _S_2 whose prototiles are an equilateral triangle (a 3-sided regular polygon) and an isosceles triangle are obtained. In this paper we extend these results presenting the study of all spherical f-tilings by equilateral triangles and scalene triangles in a particular way of adjacency. For this particular case of adjacency, we get two continuous families of f-tilings denoted by _F_1δ and _F_2δ. The combinatorial structure including the transitive properties under the action of their symmetry groups is given in Table 1.

Cite this article

Ana M. d'Azevedo Breda, Patrícia S. Ribeiro, Altino F. Santos, Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles-I. Rend. Sem. Mat. Univ. Padova 124 (2010), pp. 1–23

DOI 10.4171/RSMUP/124-1