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European Mathematical Society Publishing House
2016-09-19 17:05:48
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
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124
2010
0
Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles-I
A.M.
d'Azevedo Breda
Universidade de Aveiro, AVEIRO, PORTUGAL
Patrícia
Ribeiro
E.S.T. Setúbal, SETUBAL, PORTUGAL
Altino
Santos
Universidade de Trás-os-Montes e Alto Douro, VILA REAL, PORTUGAL
The study of dihedral f-tilings of the Euclidean sphere S2 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 S2 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 F1δ and F2δ. The combinatorial structure including the transitive properties under the action of their symmetry groups is given in Table 1.
Convex and discrete geometry
Group theory and generalizations
General
1
23
10.4171/RSMUP/124-1
http://www.ems-ph.org/doi/10.4171/RSMUP/124-1