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Algebraic properties of basic isohedral marked tilings

Published online by Cambridge University Press:  26 April 2006

GABRIELE H. GRECO
GABRIELE H. GRECO
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo (TN), Italy. e-mail: [email protected]
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Abstract

In 1977 Grünbaum and Shephard described all possible 93 types of isohedral marked tilings of the plane; 46 of them are called basic, since their induced tile group is trivial. The aim of this paper is to give an algebraic description of all basic tilings. A purely algebraic characterization of the adjacency symmetries of tiles of the 46 basic tilings is presented. Moreover, 46 related abstract definitions of two-dimensional crystallographic groups supplement and extend those of the well-known book Generators and Relations for Discrete Groups by Coxeter and Moser.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 140 , Issue 3 , May 2006 , pp. 417 - 423
Copyright
2006 Cambridge Philosophical Society

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