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- Uniform_honeycomb 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.".
- Uniform_honeycomb thumbnail Uniform_tiling_532-t012.png?width=300.
- Uniform_honeycomb wikiPageExternalLink tessel.htm.
- Uniform_honeycomb wikiPageID "23506187".
- Uniform_honeycomb wikiPageLength "5976".
- Uniform_honeycomb wikiPageOutDegree "69".
- Uniform_honeycomb wikiPageRevisionID "680211567".
- Uniform_honeycomb wikiPageWikiLink 16-cell.
- Uniform_honeycomb wikiPageWikiLink Alfredo_Andreini.
- Uniform_honeycomb wikiPageWikiLink Beltrami–Klein_model.
- Uniform_honeycomb wikiPageWikiLink Branko_Grünbaum.
- Uniform_honeycomb wikiPageWikiLink Category:Honeycombs_(geometry).
- Uniform_honeycomb wikiPageWikiLink Category:Uniform_tilings.
- Uniform_honeycomb wikiPageWikiLink Convex_uniform_honeycomb.
- Uniform_honeycomb wikiPageWikiLink Coxeter_diagram.
- Uniform_honeycomb wikiPageWikiLink Coxeter–Dynkin_diagram.
- Uniform_honeycomb wikiPageWikiLink Cubic_honeycomb.
- Uniform_honeycomb wikiPageWikiLink Facet_(geometry).
- Uniform_honeycomb wikiPageWikiLink Facet_(mathematics).
- Uniform_honeycomb wikiPageWikiLink G.C._Shephard.
- Uniform_honeycomb wikiPageWikiLink Geoffrey_Colin_Shephard.
- Uniform_honeycomb wikiPageWikiLink Geombinatorics.
- Uniform_honeycomb wikiPageWikiLink Geometry.
- Uniform_honeycomb wikiPageWikiLink George_Olshevsky.
- Uniform_honeycomb wikiPageWikiLink H._S._M._Coxeter.
- Uniform_honeycomb wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Uniform_honeycomb wikiPageWikiLink Honeycomb_(geometry).
- Uniform_honeycomb wikiPageWikiLink Isogonal_figure.
- Uniform_honeycomb wikiPageWikiLink List_of_convex_uniform_tilings.
- Uniform_honeycomb wikiPageWikiLink List_of_regular_polytopes.
- Uniform_honeycomb wikiPageWikiLink List_of_regular_polytopes_and_compounds.
- Uniform_honeycomb wikiPageWikiLink List_of_uniform_tilings.
- Uniform_honeycomb wikiPageWikiLink Norman_Johnson_(mathematician).
- Uniform_honeycomb wikiPageWikiLink Octahedron.
- Uniform_honeycomb wikiPageWikiLink Order-4_dodecahedral_honeycomb.
- Uniform_honeycomb wikiPageWikiLink Order-4_hexagonal_tiling_honeycomb.
- Uniform_honeycomb wikiPageWikiLink Paracompact_uniform_honeycomb.
- Uniform_honeycomb wikiPageWikiLink Paracompact_uniform_honeycombs.
- Uniform_honeycomb wikiPageWikiLink Poincaré_disk_model.
- Uniform_honeycomb wikiPageWikiLink Square_tiling.
- Uniform_honeycomb wikiPageWikiLink Stereographic_projection.
- Uniform_honeycomb wikiPageWikiLink Truncated_icosidodecahedron.
- Uniform_honeycomb wikiPageWikiLink Truncated_triapeirogonal_tiling.
- Uniform_honeycomb wikiPageWikiLink Truncated_triheptagonal_tiling.
- Uniform_honeycomb wikiPageWikiLink Truncated_trihexagonal_tiling.
- Uniform_honeycomb wikiPageWikiLink Uniform_4-polytope.
- Uniform_honeycomb wikiPageWikiLink Uniform_5-polytope.
- Uniform_honeycomb wikiPageWikiLink Uniform_6-polytope.
- Uniform_honeycomb wikiPageWikiLink Uniform_polyhedron.
- Uniform_honeycomb wikiPageWikiLink Uniform_polytope.
- Uniform_honeycomb wikiPageWikiLink Uniform_tiling.
- Uniform_honeycomb wikiPageWikiLink Uniform_tilings_in_hyperbolic_plane.
- Uniform_honeycomb wikiPageWikiLink Vertex-transitive.
- Uniform_honeycomb wikiPageWikiLink Vertex_configuration.
- Uniform_honeycomb wikiPageWikiLink Vertex_figure.
- Uniform_honeycomb wikiPageWikiLink Wythoff_construction.
- Uniform_honeycomb wikiPageWikiLink File:16-cell_verf.png.
- Uniform_honeycomb wikiPageWikiLink File:Cubic_honeycomb.png.
- Uniform_honeycomb wikiPageWikiLink File:Cubic_honeycomb_verf.png.
- Uniform_honeycomb wikiPageWikiLink File:Great_rhombicosidodecahedron_vertfig.png.
- Uniform_honeycomb wikiPageWikiLink File:Great_rhombitriheptagonal_tiling_vertfig.png.
- Uniform_honeycomb wikiPageWikiLink File:Great_rhombitrihexagonal_tiling_vertfig.png.
- Uniform_honeycomb wikiPageWikiLink File:H2_tiling_23i-7.png.
- Uniform_honeycomb wikiPageWikiLink File:Hyperbolic_3d_order_4_hexagonal_tiling.png.
- Uniform_honeycomb wikiPageWikiLink File:Hyperbolic_orthogonal_dodecahedral_honeycomb.png.
- Uniform_honeycomb wikiPageWikiLink File:Order-4_dodecahedral_honeycomb_verf.png.
- Uniform_honeycomb wikiPageWikiLink File:Order-4_hexagonal_tiling_honeycomb_verf.png.
- Uniform_honeycomb wikiPageWikiLink File:Stereographic_polytope_16cell.png.
- Uniform_honeycomb wikiPageWikiLink File:Uniform_polyhedron-63-t012.png.
- Uniform_honeycomb wikiPageWikiLink File:Uniform_tiling_532-t012.png.
- Uniform_honeycomb wikiPageWikiLink File:Uniform_tiling_73-t012.png.
- Uniform_honeycomb wikiPageWikiLinkText "uniform honeycomb".
- Uniform_honeycomb wikiPageWikiLinkText "uniform tessellation".
- Uniform_honeycomb wikiPageWikiLinkText "uniform tessellations".
- Uniform_honeycomb hasPhotoCollection Uniform_honeycomb.
- Uniform_honeycomb title "Uniform tessellation".
- Uniform_honeycomb urlname "UniformTessellation".
- Uniform_honeycomb wikiPageUsesTemplate Template:CDD.
- Uniform_honeycomb wikiPageUsesTemplate Template:Cite_book.
- Uniform_honeycomb wikiPageUsesTemplate Template:KlitzingPolytopes.
- Uniform_honeycomb wikiPageUsesTemplate Template:Main.
- Uniform_honeycomb wikiPageUsesTemplate Template:MathWorld.
- Uniform_honeycomb wikiPageUsesTemplate Template:Tessellation.
- Uniform_honeycomb wikiPageUsesTemplate Template:The_Geometrical_Foundation_of_Natural_Structure_(book).
- Uniform_honeycomb subject Category:Honeycombs_(geometry).
- Uniform_honeycomb subject Category:Uniform_tilings.
- Uniform_honeycomb hypernym Honeycomb.
- Uniform_honeycomb 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.".
- Uniform_honeycomb label "Uniform honeycomb".
- Uniform_honeycomb wasDerivedFrom Uniform_honeycomb?oldid=680211567.
- Uniform_honeycomb depiction Uniform_tiling_532-t012.png.
- Uniform_honeycomb isPrimaryTopicOf Uniform_honeycomb.