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A class of spherical dihedral \(f\)-tilings. (English) Zbl 1161.52014

A \(f\)-tiling \(\tau\) is said to be monohedral if it is composed by congruent cells, and dihedral if every tile of \(\tau\) is congruent to one of two fixed sets \(X\) and \(Y\) (prototiles of \(\tau\)). The classification of all dihedral triangular \(f\)-tilings of the Riemannian sphere \(S^2\) whose prototiles are an equilateral triangle and an isosceles triangle and the identification of their symmetry groups is given. It is also determined their classes of isogonality and isohedrality.

MSC:

52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
05B45 Combinatorial aspects of tessellation and tiling problems
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