A Complete List of All Convex Polyhedra Made by Gluing Regular Pentagons

TL;DR

This paper provides a comprehensive classification of convex polyhedra formed exclusively by gluing regular pentagons, introducing a novel method for analyzing their graph structures that can be applied to similar geometric problems.

Contribution

It offers a complete list of convex polyhedra made from regular pentagons and presents a new approach for deriving their graph structures from the gluing process.

Findings

Complete classification of convex pentagonal polyhedra

New method for determining polyhedral graph structures

Applicable to other geometric gluing problems

Abstract

We give a complete description of all convex polyhedra whose surface can be constructed from several congruent regular pentagons by folding and gluing them edge to edge. Our method of determining the graph structure of the polyhedra from a gluing is of independent interest and can be used in other similar settings.