A construction of inflation rules based onnfold symmetry
 K.P Nischke,
 L. Danzer
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In analogy to the wellknown tilings of the euclidean plane \(\mathbb{E}^2 \) by Penrose rhombs (or, to be more precise, to the equivalent tilings by Robinson triangles) we give a construction of an inflation rule based on thenfold symmetryD _{n}for everyn greater than 3 and not divisible by 3. For givenn the inflation factor η can be any quotient \(\mu _{n,k} : = \sin \left( {k\pi /n} \right)/\sin \left( {\pi /n} \right)\) as well as any product \(\prod {_{k = 2}^{n/2} \mu _{n,k}^{ak} ,} \) where \(\alpha _2 ,\alpha _3 ,..., \in \mathbb{N} \cup \left\{ 0 \right\}\) . The construction is based on the system ofn tangents of the wellknown deltoidD, which form angles with the ζaxis of typevπ/n. None of these tilings permits two linearly independent translations. We conjecture that they have no period at all. For some of them the Fourier transform contains a ℤmodule of Dirac deltas.
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 Title
 A construction of inflation rules based onnfold symmetry
 Journal

Discrete & Computational Geometry
Volume 15, Issue 2 , pp 221236
 Cover Date
 19960201
 DOI
 10.1007/BF02717732
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 K.P Nischke ^{(1)}
 L. Danzer ^{(1)}
 Author Affiliations

 1. Institut für Mathematik, Universität Dortmund, D44221, Dortmund, Germany