Tilings of Polygons with Similar Triangles, II
نویسندگان
چکیده
منابع مشابه
Tilings with noncongruent triangles
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.
متن کاملTiling Polygons with Lattice Triangles
Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...
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This paper studies the tilings with colored-edges triangles constructed on a triangulation of a simply connected orientable surface such that the degree of each interior vertex is even (such as, for (fundamental) example, a part of the triangular lattice of the plane). The constraints are that we only use three colors, all the colors appear in each tile and two tile can share an edge only if th...
متن کاملDomino tilings of orthogonal polygons
We consider orthogonal polygons with vertices located at integer lattice points. We show that if all of the sides of a simple orthogonal polygon without holes have odd lengths, then it cannot be tiled by dominoes. We provide similar characterizations for orthogonal polygons with sides of arbitrary length. We also give some generalizations for polygons with holes and polytopes in 3 dimensions.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1998
ISSN: 0179-5376
DOI: 10.1007/pl00009359