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Dihedral f-tilings of the sphere by rhombi and triangles

Abstract : We classify, up to an isomorphism, the class of all dihedral f-tilings of S^2, whose prototiles are a spherical triangle and a spherical rhombus. The equiangular case was considered and classified in Ana M. Breda and Altino F. Santos, Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles. Here we complete the classification considering the case of non-equiangular rhombi.
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https://hal.inria.fr/hal-00959034
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Ana Breda, Altino F. Santos. Dihedral f-tilings of the sphere by rhombi and triangles. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2005, 7, pp.123-140. ⟨hal-00959034⟩

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