Quasi-unit cell description of two-dimensional octagonal quasilattice

TL;DR

This paper introduces a cluster covering scheme to construct a two-dimensional octagonal quasilattice using a quasi-unit cell, which overlaps according to specific rules to generate the quasilattice.

Contribution

It presents a novel quasi-unit cell approach for modeling octagonal quasilattices, extending concepts from five-fold quasicrystals.

Findings

Successful identification of a two-color quasi-unit cell

Development of a covering scheme with specific overlap rules

Generation of a perfect octagonal quasilattice

Abstract

We present a cluster covering scheme to construct the two-dimensional octagonal quasilattice. A quasi-unit cell is successfully found which is a two-color cluster similar to the Gummelt's two-color decagon in five-fold quasilattice. The quasi-unit cells overlap each other following certain covering rules and thus lead to a perfect octagonal quasilattice.