Paper Info
Title
Torus square tilings.
Abstract
We consider periodic square tilings of the plane. By extending a formalism introduced in 1940 for tiling of rectangles by squares we build a correspondence between periodic plane maps endowed with a periodic harmonic vector and periodic square tilings satisfying a regularity condition. The space of harmonic vectors is isomorphic to the first homology group of a torus. So, periodic plane square tilings are described by two parameters and the set of parameters is split into angular sectors. The correspondence between symmetry of the square tiling and symmetry of the corresponding plane map and harmonic vector is discussed and a method for enumerating the regular periodic plane square tilings having orbits of squares is outlined.
Year
DOI
Venue
2012
10.1007/s00200-012-0178-4
Appl. Algebra Eng. Commun. Comput.
Keywords
DocType
Volume
Square tiling,Harmonic vectors,Hodge theory,Electrical network,05B45,52C20
Journal
23
Issue
ISSN
Citations 
5-6
0938-1279
0
PageRank 
References 
Authors
0.34
1
1
Name
Order
Citations
PageRank
Mathieu Dutour Sikiric1184.50