Uniform tessellation

In mathematics, a uniform tessellation is a tessellation of a "d"-dimensional space, or a (hyper)surface, such that all its vertices are identical, i.e., there is the same combination and arrangement of faces at each vertex.

They can be named by a vertex figure, listing the sequence of faces around every vertex. For example 4.4.4.4 represents a regular tessellation, a square tiling, with 4 squares around each vertex. They can also be named by a Wythoff symbol as well as Coxeter-Dynkin diagrams.

When applied to Euclidean space, the tessellation is most often assumed to be by polyhedra. Examples of 3D regular tessellations are those of layers of right prisms according to the three regular tessellations in 2D; that with square cuboids is in a way the most regular, especially with cubes, because then it is congruent in three independent directions.

Examples

When applied to surfaces, uniform tessellations are an important notion for Nonuniform rational B-splines (NURBS).

ee also

* Uniform tiling
* List of uniform tilings
* Uniform tilings in hyperbolic plane
* Honeycomb (geometry)
* Wythoff construction
* Convex uniform honeycomb
* List of regular polytopes

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

Tessellation — A tessellation of pavement A honeycomb is an example of a t … Wikipedia
Uniform tiling — In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the… … Wikipedia
Uniform polytope — A uniform polytope is a vertex transitive polytope made from uniform polytope facets. A uniform polytope must also have only regular polygon faces.Uniformity is a generalization of the older category semiregular, but also includes the regular… … Wikipedia
Uniform 2 k1 polytope — In geometry, 2k1 polytope or {32,k,1} is a uniform polytope in n dimensions (n = k+4) constructed from the En Coxeter group. The family was named by Coxeter as 2k1 by its bifurcating Coxeter Dynkin diagram, with a single ring on the end of the 2… … Wikipedia
Uniform 1 k2 polytope — In geometry, 1k2 polytope or {31,k,2} is a uniform polytope in n dimensions (n = k+4) constructed from the En Coxeter group. The family was named by Coxeter as 1k2 by its bifurcating Coxeter Dynkin diagram, with a single ring on the end of the 1… … Wikipedia
Convex uniform honeycomb — The alternated cubic honeycomb is one of 28 space filling uniform tessellations in Euclidean 3 space, composed of alternating yellow tetrahedra and red octahedra. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three … Wikipedia
List of uniform polyhedra — Uniform polyhedra and tilings form a well studied group. They are listed here for quick comparison of their properties and varied naming schemes and symbols.This list includes: * all 75 nonprismatic uniform polyhedra; * a few representatives of… … Wikipedia
Convex uniform honeycombs in hyperbolic space — The {5,3,4} honeycomb in 3D hyperbolic space, viewed in perspective In geometry, a convex uniform honeycomb is a tessellation of convex uniform polyhedron cells. In 3 dimensional hyperbolic space there are nine Coxeter group f … Wikipedia
Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides … Wikipedia
Triangular tiling — Type Regular tiling Vertex configuration 3.3.3.3.3.3 (or 36) Schläfli symbol(s) {3,6} {3[3]} … Wikipedia

Academic Dictionaries and Encyclopedias

Uniform tessellation

Look at other dictionaries:

Share the article and excerpts

Academic Dictionaries and Encyclopedias

Wikipedia

Uniform tessellation

Look at other dictionaries:

Share the article and excerpts

Direct link