About: Uniform honeycomb

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In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets. All of its vertices are identical and there is the same combination and arrangement of faces at each vertex. Its dimension can be clarified as n-honeycomb for an n-dimensional honeycomb. An n-dimensional uniform honeycomb can be constructed on the surface of n-spheres, in n-dimensional Euclidean space, and n-dimensional hyperbolic space. A 2-dimensional uniform honeycomb is more often called a uniform tiling or uniform tessellation.

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rdfs:label	Uniform honeycomb (en)
rdfs:comment	In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets. All of its vertices are identical and there is the same combination and arrangement of faces at each vertex. Its dimension can be clarified as n-honeycomb for an n-dimensional honeycomb. An n-dimensional uniform honeycomb can be constructed on the surface of n-spheres, in n-dimensional Euclidean space, and n-dimensional hyperbolic space. A 2-dimensional uniform honeycomb is more often called a uniform tiling or uniform tessellation. (en)
foaf:depiction
dcterms:subject	Honeycombs (geometry) Uniform tilings
Wikipage page ID	23506187 (xsd:integer)
Wikipage revision ID	1119353880 (xsd:integer)
Link from a Wikipage to another Wikipage	Beltrami–Klein model Branko Grünbaum Alfredo Andreini List of uniform tilings Cubic honeycomb Uniform 4-polytope Uniform polyhedron Vertex configuration Uniform 6-polytope 16-cell Honeycombs (geometry) Coxeter–Dynkin diagram Truncated triapeirogonal tiling Geometry Convex uniform honeycomb Order-4 hexagonal tiling honeycomb Stereographic projection Truncated icosidodecahedron Truncated trihexagonal tiling Uniform tilings Euclidean space Norman Johnson (mathematician) Hyperbolic space Vertex figure Honeycomb (geometry) Uniform 5-polytope Uniform polytope Poincaré disk model H. S. M. Coxeter Facet (mathematics) Octahedron Order-4 dodecahedral honeycomb Vertex (geometry) Geombinatorics Square tiling Wythoff construction Truncated triheptagonal tiling Uniform tilings in hyperbolic plane Uniform tiling List of regular polytopes Paracompact uniform honeycomb Coxeter diagram Vertex-transitive
Link from a Wikipage to an external page	http://www.orchidpalms.com/polyhedra/tessellations/tessel.htm https://archive.org/details/isbn_0716711931
sameAs	Uniform honeycomb Uniform honeycomb Uniform honeycomb Uniform honeycomb
dbp:wikiPageUsesTemplate	dbt:CDD dbt:Cite_book dbt:KlitzingPolytopes dbt:Main dbt:Math dbt:MathWorld dbt:Mvar dbt:Short_description dbt:Tessellation dbt:The_Geometrical_Foundation_of_Natural_Structure_(book)
thumbnail	wiki-commons:Special:FilePath/Uniform_tiling_532-t012.png?width=300
title	Uniform tessellation (en)
urlname	UniformTessellation (en)
has abstract	In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets. All of its vertices are identical and there is the same combination and arrangement of faces at each vertex. Its dimension can be clarified as n-honeycomb for an n-dimensional honeycomb. An n-dimensional uniform honeycomb can be constructed on the surface of n-spheres, in n-dimensional Euclidean space, and n-dimensional hyperbolic space. A 2-dimensional uniform honeycomb is more often called a uniform tiling or uniform tessellation. Nearly all uniform tessellations can be generated by a Wythoff construction, and represented by a Coxeter–Dynkin diagram. The terminology for the convex uniform polytopes used in uniform polyhedron, uniform 4-polytope, uniform 5-polytope, uniform 6-polytope, uniform tiling, and convex uniform honeycomb articles were coined by Norman Johnson. Wythoffian tessellations can be defined by a vertex figure. For 2-dimensional tilings, they can be given by a vertex configuration 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. In general an n-dimensional uniform tessellation vertex figures are define by an (n–1)-polytope with edges labeled with integers, representing the number of sides of the polygonal face at each edge radiating from the vertex. (en)
gold:hypernym	Honeycomb

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