Some tilings of the plane whose singular points form a perfect set
Proc. Amer. Math. Soc. 89 (1983), 477-479
Primary 52A45; Secondary 05B45
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Abstract: Let be a tiling of the plane such that for every tile of there correspond a tile of (not necessarily unique) and an integer (depending on and ), , such that meets in connected components. Then the set of singular points of is a nowhere dense, perfect set.
Grünbaum and G.
C. Shephard, Tilings and patterns, A Series of Books in the
Mathematical Sciences, W. H. Freeman and Company, New York, 1989. An
Valette, Tilings of the plane by topological disks, Geom.
Dedicata 11 (1981), no. 4, 447–454. MR
- B. Grünbaum and G. C. Shepard, Tilings and patterns, Freeman, San Francisco, Calif. (to appear). MR 992195 (90a:52027)
- Alain Valette, Tilings of the plane by topological disks, Geom. Dedicata 11 (1981), 447-454. MR 637919 (82m:05032)
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