Patch-determined tilings

Author:

Grünbaum B.,Shephard G. C.

Abstract

A tiling of the plane is a family of sets, called tiles, that cover the plane without gaps or overlaps. Usually we are concerned with tilings whose tiles are of a small number of different shapes; familiar examples are the regular and uniform tilings (see, for example, [1]).Although the mathematical theory of tiling is very old, it still contains a rich supply of interesting and challenging problems. The purpose of this article is to describe some of these. In many cases the mathematical aspect is enhanced by the aesthetic appeal of the resulting tilings.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference6 articles.

1. XXIX.—Semi-regular Networks of the Plane in Absolute Geometry

2. Sur les pavages à l’aide de polygones réguliers;Levy;Bull. Soc. philomath. Paris,1891

3. Central tessellations;Goldberg;Scr. math.,1955

4. On Paving the Plane

5. On tessellating the plane with convex polygon tiles;Gardner;Scient. Am.,1975

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1. A Sticker Album for Tilers (Collector’s Edition);The Mathematical Intelligencer;2023-12-09

2. Solutions to Seven and a Half Problems on Tilings;The Electronic Journal of Combinatorics;2023-06-30

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