Lattice representations of Penrose tilings of the plane

TL;DR

This paper explores lattice-based representations of Penrose tilings in multiple dimensions, discussing symmetries, visualization techniques, and efficient data storage methods for reconstructing these non-periodic tilings.

Contribution

It introduces lattice representations of Penrose tilings across different dimensions and analyzes their symmetries and visualization approaches, including data storage strategies.

Findings

Vertices lie on lattices in these representations

Symmetries of Penrose tilings are discussed

Methods for visualizing and storing tilings are proposed

Abstract

Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed. The question of efficiently storing the information necessary to reconstruct a tiling is addressed.