Tilings of the Sphere by Congruent Pentagons I: Edge Combinations $a^2{b}^{2}c$ and $a^{3}bc$

Erxiao Wang, Min Yan

We develop the basic tools for classifying edge-to-edge tilings of the sphere by congruent pentagons. Then we prove that, for the edge combination $a^2{b}^{2}c$, such tilings are three…