Discrete Mathematics & Theoretical Computer Science, Vol 7 (2005)

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Dihedral f-tilings of the sphere by rhombi and triangles

Ana M. Breda, Altino F. Santos


We classify, up to an isomorphism, the class of all dihedral f-tilings of S2, 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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