In geometry, the icosahedral honeycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {3,5,3}, there are three icosahedra around each edge, and 12 icosahedra around each vertex, in a regular dodecahedral vertex figure.
A geometric honeycomb is a space-filling 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.
Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space.
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In geometry, the icosahedralhoneycomb is one of four compact, regular, space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli...
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate...
compact, paracompact and noncompact hyperbolic tilings, such as the icosahedralhoneycomb {3,5,3}, and order-5 pentagonal tiling {5,5}. In 2 dimensions, all...
hyperbolic honeycombs, and it is not known how many are left to be discovered. Two have been listed above as diminishings of the icosahedralhoneycomb {3,5...
prototiles). A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical...
regular polyhedra: t{q,p}. Two are honeycombs on the 3-sphere, one a honeycomb in Euclidean 3-space, and two are honeycombs in hyperbolic 3-space. uniform...
a local icosahedral order. The icosahedral order is in equilibrium in the liquid state for the stable quasicrystals, whereas the icosahedral order prevails...
hyperbolic space-filling tessellation, the bitruncated order-5 dodecahedral honeycomb. This polyhedron can be constructed from an icosahedron by truncating...
cell-transitive hyperbolic space-filling tessellation, the bitruncated icosahedralhoneycomb. The area A and the volume V of a truncated dodecahedron of edge...
represents the vertex figure of a hyperbolic uniform honeycomb, the partially diminished icosahedralhoneycomb, pd{3,5,3}, with 12 pentagonal antiprisms and...
4-polytopes and honeycombs, {p,3,3} with tetrahedral vertex figures, {3,3}. The tesseract is also in a sequence of regular 4-polytope and honeycombs, {4,3,p}...
geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges, and vertices, creating new facets...
In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23...
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