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Cubic-octahedral Honeycomb
In the geometry of Hyperbolic space, hyperbolic 3-space, the cubic-octahedral honeycomb is a compact uniform honeycomb (geometry), honeycomb, constructed from cube, octahedron, and cuboctahedron cells, in a rhombicuboctahedron vertex figure. It has a single-ring Coxeter-Dynkin diagram, Coxeter diagram, , and is named by its two regular cells. Images Wide-angle perspective views: File:H3 4343-0010 center ultrawide.png, Centered on cube File:H3 4343-1000 center ultrawide.png, Centered on octahedron File:H3 4343-0001 center ultrawide.png, Centered on cuboctahedron It contains a subgroup H2 tiling, the alternated order-4 hexagonal tiling, , with vertex figure (3.4)4. : Symmetry A lower symmetry form, index 6, of this honeycomb can be constructed with [(4,3,4,3*)] symmetry, represented by a trigonal trapezohedron fundamental domain, and Coxeter diagram . This lower symmetry can be extended by restoring one mirror as . Related honeycombs There are 5 related uniform honeycomb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Honeycombs In Hyperbolic Space
In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedron, uniform polyhedral Cell (geometry), cells. In 3-dimensional hyperbolic space there are nine Coxeter group families of compact convex uniform honeycombs, generated as Wythoff constructions, and represented by permutations of Coxeter-Dynkin diagram#Application with uniform polytopes, rings of the Coxeter diagrams for each family. Hyperbolic uniform honeycomb families Honeycombs are divided between compact and paracompact forms defined by Coxeter groups, the first category only including finite cells and vertex figures (finite subgroups), and the second includes affine subgroups. Compact uniform honeycomb families The nine compact Coxeter groups are listed here with their Coxeter diagrams, in order of the relative volumes of their Fundamental domain, fundamental simplex domains.Felikson, 2002 These 9 families generate a total of 76 unique uniform honeycombs. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
