Tilings of the Sphere by Congruent Pentagons III: Edge Combination $a^5$

Abstract

There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.

arXiv comment48 pages, 22 figures