Symmetry Structure of the Elser-Sloane Quasicrystal

TL;DR

This paper analyzes the symmetry structure of the 4D Elser-Sloane quasicrystal, derived from the E8 lattice, using an 8D torus parametrization to understand its point and inflation symmetries.

Contribution

It provides an explicit analysis of the symmetry structure of the Elser-Sloane quasicrystal through torus parametrization.

Findings

Explicit description of point symmetry group

Analysis of inflation symmetry structure

Connection to E8 lattice and cut-and-project method

Abstract

The 4D quasicrystal of Elser and Sloane, obtained from the root lattice E8 by the cut-and-project method, can be parametrized by the points of an 8D torus. This allows for an explicit analysis of its point and inflation symmetry structure.