Superquasicrystals: selfsimilar ordered structures with non-crystallographic point symmetries

TL;DR

This paper introduces superquasicrystals, a new class of aperiodic ordered structures with non-crystallographic symmetries, constructed via a systematic method involving higher-dimensional limit-periodic structures and super-Bravais-lattices.

Contribution

It presents a novel systematic method for constructing superquasicrystals, expanding the understanding of aperiodic structures beyond traditional quasicrystals.

Findings

Superquasicrystals exhibit strong selfsimilarities.

A two-dimensional octagonal superquasicrystal example is provided.

Superquasicrystals are sections of higher-dimensional limit-periodic structures.

Abstract

We present a systematic method of constructing limit-quasiperiodic structures with non-crystallographic point symmetries. Such structures are different aperiodic ordered structures from quasicrystals, and we call them "superquasicrystals". They are sections of higher-dimensional limit-periodic structures constructed on "super-Bravais-lattices". We enumerate important super-Bravais-lattices. Superquasicrystals with strong selfsimilarities form an important subclass. A simplest example is a two-dimensional octagonal superquasicrystal.