Tiling groups: New applications in the triangular lattice
نویسندگان
چکیده
منابع مشابه
Coordinates for a new triangular tiling of the hyperbolic plane
In this paper we define an infinite family of triangular tilings of the hyperbolic plane defined by two parameters ranging in the natural numbers and we give a uniform way to define coordinates for locating the triangles
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Let L and K be two full rank lattices in R. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles R by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) ≤ v(K) then there exists a measurable set Ω such that it tiles by L and packs by K. Using th...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1998
ISSN: 0179-5376,1432-0444
DOI: 10.1007/pl00009382