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arXiv · 1208.1845

A Single Cluster Covering for Dodecagonal Quasiperiodic Structure

Longguang Liao·Zexian Cao
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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°-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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Longguang Liao, Zexian Cao. 2012-08-09. A Single Cluster Covering for Dodecagonal Quasiperiodic Structure. https://doi.org/10.1088/0256-307x%2F30%2F2%2F026102

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