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Triangular spherical dihedral f-tilings: the $(\pi/2, \pi/3, \pi/4)$ and $(2\pi/3, \pi/4, \pi/4)$ family
Volume 61, no. 2 (2020), pp. 367–387

Abstract

We classify all the dihedral f-tilings with spherical triangles $\big(\frac{\pi}{2}, \frac{\pi}{3}, \frac{\pi}{4}\big)$ and $\big(\frac{2\pi}{3}, \frac{\pi}{4}, \frac{\pi}{4}\big)$, and give the combinatorial structure, including the symmetry group of each tiling.