Search results
Results from the WOW.Com Content Network
Under relatively general conditions (the space is a possibly infinite-dimensional uniformly convex space, there can be infinitely many sites of a general form, etc.) Voronoi cells enjoy a certain stability property: a small change in the shapes of the sites, e.g., a change caused by some translation or distortion, yields a small change in the ...
The tessellations created by bonded brickwork do not obey this rule. Among those that do, a regular tessellation has both identical [a] regular tiles and identical regular corners or vertices, having the same angle between adjacent edges for every tile. [14] There are only three shapes that can form such regular tessellations: the equilateral ...
Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure: not itself an element of a polytope, but a diagram showing how the elements meet.
Regular tetrahedra alone do not tessellate (fill space), but if alternated with regular octahedra in the ratio of two tetrahedra to one octahedron, they form the alternated cubic honeycomb, which is a tessellation. Some tetrahedra that are not regular, including the Schläfli orthoscheme and the Hill tetrahedron, can tessellate.
For example: 3 6; 3 6; 3 4.6, tells us there are 3 vertices with 2 different vertex types, so this tiling would be classed as a ‘3-uniform (2-vertex types)’ tiling. Broken down, 3 6 ; 3 6 (both of different transitivity class), or (3 6 ) 2 , tells us that there are 2 vertices (denoted by the superscript 2), each with 6 equilateral 3-sided ...
Polyhedra are the three dimensional correlates of polygons. They are built from flat faces and straight edges and have sharp corner turns at the vertices. Although a cube is the only regular polyhedron that admits of tessellation, many non-regular 3-dimensional shapes can tessellate, such as the truncated octahedron.
A dodecahedron can be considered a regular tiling of 12 pentagons on the surface of a sphere, with Schläfli symbol {5,3}, having three pentagons around each vertex. One may also consider a degenerate tiling by two hemispheres, with the great circle between them subdivided into five equal arcs, as a pentagonal tiling with Schläfli symbol {5,2}.
This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed