Dihedral f-tilings of the sphere by spherical triangles and equiangular well-centered quadrangles
A dihedral f-tiling of the Euclidean sphere consists of a decomposition of the sphere by polygons congruent to two fixed non-congruent polygons, the prototiles, with each vertex of even valency and the alternating angles at each vertex adding up to \(\pi\). The authors classify similar tilings where the prototiles are spherical triangles and well centered quadrangles with internal angles all congruent. This classification involves the cases where the triangle is equilateral, isosceles or scalene and the quadrangle has congruent adjacent sides or non-congruent adjacent sides.
scientific article; zbMATH DE number 2100234