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Honeycomb (geometry) In geometry, a honeycomb is a space filling or close packing of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n -honeycomb for a honeycomb of n -dimensional space.
C. Cantellated 24-cell honeycomb. Cantitruncated 24-cell honeycomb. Convex uniform honeycomb. Template:Cubic cell tessellations. Cubic honeycomb honeycomb. Cyclotruncated 5-simplex honeycomb. Cyclotruncated 6-simplex honeycomb.
Uniform honeycomb. 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 ...
Properties. edge-transitive, face-transitive, cell-transitive. The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler ...
In the geometry of hyperbolic 4-space, the cubic honeycomb honeycomb is one of two paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite facets, whose vertices exist on 3- horospheres and converge to a single ideal point at infinity. With Schläfli symbol {4,3,4,3}, it has three cubic ...
In hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) of hyperbolic 3-space. With Schläfli symbol {5,3,4}, it has four dodecahedra around each edge, and 8 dodecahedra around each vertex in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes.