منابع مشابه
Spherical Tiling by Congruent Pentagons
We consider tilings of the sphere by congruent pentagons. The basic example is dodecahedron, which has 12 pentagonal tiles. To simplify the problem, we assume the tiling is edge-to-edge and all vertices have degree ≥ 3.
متن کاملSpherical tiling by 12 congruent pentagons
a r t i c l e i n f o a b s t r a c t The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons. In this paper, we classify the simplest case, which is the edge-to-edge tilings of the 2-dimensional sphere by 12 congruent penta...
متن کاملTiling Polyhedra with Tetrahedra
When solving an algorithmic problem involving a polyhedron in R, it is common to start by partitioning the given polyhedron into simplier ones. The most common process is called triangulation and it refers to partitioning a polyhedron into tetrahedra in a face-to-face manner. In this paper instead of triangulations we will consider tilings by tetrahedra. In a tiling the tetrahedra are not requi...
متن کاملTiling a Square with Eight Congruent Polyominoes
The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangular order 8, and asks if it can be generalized to a family of rectifiable polyominoes. Here we show...
متن کاملTiling a Triangle with Congruent Triangles
We investigate the problem of cutting a triangle ABC into N congruent triangles (the “tiles”), which may or may not be similar to ABC. We wish to characterize the numbers N for which some triangle ABC can be tiled by N tiles, or more generally to characterize the triples (N,T ) such that ABC can be N-tiled using tile T . In the first part of the paper we exhibit certain families of tilings whic...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1974
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1974-13524-x