Icosahedral multi-component model sets

TL;DR

This paper demonstrates how to construct icosahedral multi-component model sets using the strip projection method, reducing the superspace dimension to 6 when cluster coordinates are in Q[√5].

Contribution

It introduces a method to define icosahedral model sets with reduced superspace dimension leveraging algebraic properties of cluster coordinates.

Findings

Superspace dimension can be reduced to 6 for certain clusters.

The method applies to clusters with coordinates in Q[√5].

Provides a framework for modeling quasiperiodic packings.

Abstract

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.