Article contents
Finite edge-to-edge tilings by convex polygons
Part of:
Discrete geometry
Published online by Cambridge University Press: 26 February 2010
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
- Copyright
- Copyright © University College London 2001
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
- 2
- Cited by