A Single Cluster Covering for Dodecagonal Quasiperiodic Structure

TL;DR

This paper introduces a novel single cluster covering scheme for the dodecagonal quasiperiodic ship tiling, constructed from a single prototile with matching rules, aiding the study of dodecagonal quasicrystals.

Contribution

It presents the first single cluster covering scheme for dodecagonal quasiperiodic structures using a single prototile and deflation method.

Findings

Constructed ship tiling from one prototile with matching rules

Identified fourteen vertical configurations fulfilling deflation closure

Facilitates physical property studies of dodecagonal quasicrystals

Abstract

Single cluster covering approach provides a plausible mechanism for the formation and stability of octagonal and decagonal quasiperiodic structures. For dodecagonal quasiperiodic pattern such a single cluster covering scheme is still unavailable. Here we demonstrated that the ship tiling, one of the dodecagonal quasiperioidic structures, can be constructed from one single prototile with matching rules. A deflation procedure is devised by assigning proper orientations to the tiles present in the ship tiling including regular triangle, 30{\deg}-rhombus and square, and fourteen types of vertical configurations have been identified in the deflated pattern, which fulfill the closure condition under deflation and all result in a T-cluster centered at vertex. This result can facilitate the study of physical properties of dodecagonal quasicrystals.