About a new splitting for the algorithmic study of the tilings $\{p,q\}$ of the hyperbolic plane when $q$ is odd

TL;DR

This paper introduces two novel methods for splitting the hyperbolic plane to algorithmically construct tilings p,q when q is odd, building on previous results about hyperbolic tilings.

Contribution

The paper presents new splitting techniques for hyperbolic plane tilings p,q with odd q, enabling improved algorithmic construction of these tilings.

Findings

Two new splitting methods for hyperbolic tilings p,q with odd q

Enhanced algorithms for constructing p,q tilings

Extension of previous hyperbolic tiling results

Abstract

In this paper, we remind previous results about the tilings $\{p,q\}$ of the hyperbolic plane. We introduce two new ways to split the hyperbolic plane in order to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.