Construction of the continuous hull for the combinatorics of a regular pentagonal tiling of the plane

TL;DR

This paper constructs a continuous hull for a regular pentagonal tiling of the plane, extending previous work on the discrete hull to a continuous setting, which enhances understanding of the tiling's geometric and combinatorial properties.

Contribution

It introduces a novel method for constructing a continuous hull for a pentagonal tiling, building upon prior discrete hull constructions to provide a more comprehensive geometric framework.

Findings

Successfully constructed the continuous hull for the pentagonal tiling

Bridged the gap between discrete and continuous combinatorial models

Enhanced understanding of the tiling's geometric structure

Abstract

In the article "Construction of the discrete hull for the combinatorics of a regular pentagonal tiling of the plane" we gave the construction of a discrete hull for a combinatorial pentagonal tiling of the plane. In this paper, we give the construction of a continuous hull for the same combinatorial tiling.