Right triangular spherical dihedral f--tilings: the (pi/2,pi/3,pi/5), (pi/2,2pi/5,pi/5) family
Avelino, Catarina P.; Santos, Altino F.
Journal of Geometry, 102(1-2) (2011), 1-17
http://cmutad.utad.pt/files/rightTriangularDiedralF-TilingsSphereAltinoAvelino9jan2011.pdf
The classification of all dihedral f-tilings of the Riemannian sphere S2, whose prototiles are two right triangles with at least one isosceles, is given. The combinatorial structure and the symmetry group of each tiling is also achieved.
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