# Pentagonal Subdivision

## TL;DR

This paper develops a comprehensive theory for subdividing quadrilateral tilings into pentagons on various surfaces and applies it to analyze pentagonal and double pentagonal tilings.

## Contribution

It introduces a new theoretical framework for pentagonal subdivision of quadrilateral tilings on both orientable and non-orientable surfaces.

## Key findings

- Established conditions for pentagonal subdivision on different surfaces
- Provided classifications of pentagonal tilings based on subdivision theory
- Applied the theory to solve specific tiling problems

## Abstract

We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those related to pentagonal or double pentagonal subdivisions.