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The equivalence of two face-centred icosahedral tilings with respect to local derivability

J Roth

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The author demonstrates show two tilings with face-centred icosahedral symmetry can be derived from one another by using only local information. The tiling under consideration are the zonohedral tiling proposed by Socolar and Steinhardt, which is closely related to the original three-dimensional rhombohedral tiling, and the tetrahedral tiling of Danzer. Both tilings have matching rules, and his proof is based on this property.


PACS

61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling

61.44.Br Quasicrystals

MSC

52C23 Quasicrystals, aperiodic tilings

Subjects

Condensed matter: structural, mechanical & thermal

Dates

Issue 7 (7 April 1993)



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