A Single Cluster Covering for Dodecagonal Quasiperiodic Structure

A Single Cluster Covering for Dodecagonal Quasiperiodic Structure

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...

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Veröffentlicht in:arXiv.org 2012-08
Hauptverfasser: Liao, Longguang, Cao, Zexian
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Clusters
Physical properties
Physics - Other Condensed Matter
Quasicrystals
Tiling
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description 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.
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subjects Clusters
Physical properties
Physics - Other Condensed Matter
Quasicrystals
Tiling
title A Single Cluster Covering for Dodecagonal Quasiperiodic Structure
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