Tilings of the Sphere by Congruent Pentagons II: Edge Combination $a^3b^2$

TL;DR

This paper classifies all edge-to-edge tilings of the sphere using congruent pentagons with the specific edge combination a^3b^2, identifying fifteen distinct tilings including families and modifications.

Contribution

It provides a complete classification of sphere tilings by congruent pentagons with a^3b^2 edge combination, detailing fifteen unique tilings.

Findings

Five one-parameter families of pentagonal subdivision tilings

Ten flip modifications of three special cases

Complete enumeration of tilings with the given edge combination

Abstract

There are fifteen edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^3b^2$: five one-parameter families of pentagonal subdivision tilings, and ten flip modifications of three special cases of two pentagonal subdivision tilings.