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Finite edge-to-edge tilings by convex polygons

Part of: Discrete geometry

Published online by Cambridge University Press:  26 February 2010

Roswitha Blind  and
G. C. Shephard
Roswitha Blind
Affiliation:
Waldburgstraße 88, 70563 Stuttgart, Germany E-mail: [email protected].
G. C. Shephard
Affiliation:
17 Mill Green, Stoke Holy Cross, Norwich NR 14 8PB, England, U.K. E-mail: [email protected].
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Abstract

A tiling of a convex m-gon by a finite number r of convex n-gons is said to be of type <m, n, r>. The Main Theorem of this paper gives necessary and sufficient conditions on m, n and r for a tiling of type <m, n, r> to exist.

MSC classification

Secondary: 52C20: Tilings in $2$ dimensions
Type
Research Article
Information
Mathematika , Volume 48 , Issue 1-2 , December 2001 , pp. 25 - 50
Copyright
Copyright © University College London 2001

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References

1.Bernheim, B.. Partitions of convex polygons into pentagons (Hebrew). Riveon Lematematika, 1 (1947), 95–98 {MR 9-152}.Google Scholar
2.Bernheim, B. and Motzkin, Th.. A criterion for divisibility of n-gons into k-gons. Comment. Math. Helv., 22 (1949), 93–102. {MR 10-394}.Google Scholar
3.Bleicher, M. N.. Decomposition of a k l-gons. Mitt. Math. Sent. Giessen, 166 (1984), 1–16. {MR 86e51029}.Google Scholar
4.Grünbaum, B. (with the cooperation of Victor Klee, M.A. Perles and G. C. Shephard), Convex Polytopes. Interscience Publishers (Wiley and Sons), London-New York-Sydney (1967).Google Scholar
5.Grunbaum, B. and Barnette, D.. Preassigning the shape of a face. Pacific J. Math., 32 (1970), 299–306. {MR 41-4377}.Google Scholar
6.Hertel, E.. Zerlegungen von Polygonen, Beitrcige Algebra Geom., 29 (1989), 219–231. {MR 96k51034}.Google Scholar
7.Mahlo, P.. Topologische Untersuchungen tiber Zerlegung in ebene und spharische Polygone. Dissertation (Halle), 1908Google Scholar