Geodesic
Dihedral f-tilings of the sphere by rhombi and triangles
Discrete mathematics & theoretical computer science, Tome 7 (2005).

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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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     author = {Breda, Ana and Santos, Altino F.},
     title = {Dihedral f-tilings of the sphere by rhombi and triangles},
     journal = {Discrete mathematics & theoretical computer science},
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     year = {2005},
     doi = {10.46298/dmtcs.348},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.348/}
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Breda, Ana; Santos, Altino F. Dihedral f-tilings of the sphere by rhombi and triangles. Discrete mathematics & theoretical computer science, Tome 7 (2005). doi : 10.46298/dmtcs.348. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.348/

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