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On the discretization of problems involving periodic planar tilings

✍ Scribed by Bénard, André ;Diaz, Alejandro R.

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
223 KB
Volume
17
Category
Article
ISSN
1069-8299

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✦ Synopsis

Abstract

Features related to the discretization of problems characterized by simple periodic tilings using cells of various shapes are discussed. Various cell geometries that tile the plane periodically are considered. Equivalent problems are identified, where the discretization can take place on a parallelogram, regardless of the shape of the original cell. These equivalent problems also suggest a numbering of the equations that results in matrices with interesting and useful properties. Copyright © 2001 John Wiley & Sons, Ltd.

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✍ Sándor Szabó 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 440 KB

Let us reflect an n-dimensional cube in all its faces. The 2n + 1 cubes obtained form a so-called n-dimensional cross. KBrteszi [l] raised the question whether it is possible to construct a tiling of the n-dimensional space dimensional crosses. We say that this such a tiling is regular if neighbour