Geodesic
S^2 coverings by isosceles and scalene triangles – adjacency case I
Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 419-443.

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The aim of this paper is the study and classification of spherical f-tilings by scalene triangles T and isosceles triangles T′. Due to the complexity of this wide class of tilings, we consider a subclass performed by the adjacency of the shortest side of T and the longest side of T′. It consists of seven families of f-tilings (four families with one discrete parameter and one continuous parameter, two families with one discrete parameter and one sporadic f-tiling). We also analyze the combinatorial structure of all these families of f-tilings, as well as the group of symmetries of each tiling and the transitivity classes of isohedrality and isogonality.
DOI : 10.26493/1855-3974.1401.7d9
Keywords: Dihedral f-tilings, combinatorial properties, spherical trigonometry, symmetry groups 
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Catarina P. Avelino; Altino F. Santos. S^2 coverings by isosceles and scalene triangles – adjacency case I. Ars Mathematica Contemporanea, Tome 16 (2019) no. 2, pp. 419-443. doi : 10.26493/1855-3974.1401.7d9. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1401.7d9/

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