S2 coverings by isosceles and scalene triangles – adjacency case I

Catarina P. Avelino, Altino F. Santos

Abstract


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.


Keywords


Dihedral f-tilings, combinatorial properties, spherical trigonometry, symmetry groups

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DOI: https://doi.org/10.26493/1855-3974.1401.7d9

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications