The order-6 dodecahedral honeycomb is one of 11 paracompact regular honeycombs in hyperbolic 3-space. It is paracompact because it has vertex figures composed...
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hyperbolic geometry, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) of hyperbolic 3-space...
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hyperbolic geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space...
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its regular dual, the order-6 dodecahedral honeycomb. The order-5 hexagonal tiling honeycomb has a related alternation honeycomb, represented by ↔ , with...
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20 cubes around each vertex. It is dual with the order-4 dodecahedral honeycomb. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional...
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List of mathematical shapes (section Honeycombs)
honeycomb Order-4 dodecahedral honeycomb Order-5 dodecahedral honeycomb Order-5 cubic honeycomb Icosahedral honeycomb Order-3 icosahedral honeycomb Order-4...
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honeycombs with {p,6,3} Schläfli symbol, and dodecahedral vertex figures: In the geometry of hyperbolic 3-space, the order-6-3 pentagonal honeycomb or...
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of hyperbolic 3-space, the order-6-4 square honeycomb (or 4,6,4 honeycomb) a regular space-filling tessellation (or honeycomb) with Schläfli symbol {4,6...
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parallelohedra: Cubic honeycomb (or variations: cuboid, rhombic hexahedron or parallelepiped) Hexagonal prismatic honeycomb Rhombic dodecahedral honeycomb Elongated...
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tiling cells. Convex uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes,...
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List of regular polytopes (redirect from Order-3 120-cell honeycomb)
constructionally related to prismatic uniform honeycombs by truncation operations. They are higher-dimensional analogues of the order-2 apeirogonal tiling and apeirogonal...
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hexagonal tiling cells: This honeycomb is also related to the 16-cell, cubic honeycomb and order-4 dodecahedral honeycomb, all of which have octahedral...
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honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973...
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Elongated dodecahedron (redirect from Elonagated rhombic dodecahedral honeycomb)
related to the rhombic dodecahedral honeycomb with an elongation of zero. Projected normal to the elongation direction, the honeycomb looks like a square...
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colors of cells. Convex uniform honeycombs in hyperbolic space List of regular polytopes Infinite-order dodecahedral honeycomb Coxeter, Regular Polytopes,...
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120 with a dodecahedral fundamental domain. There are also 23 paracompact Coxeter groups of rank 4 that produce paracompact uniform honeycombs with infinite...
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cross-section through xi = n is a rhombic dodecahedral honeycomb, and the cross-section through xi = n + 1/2 is a cubic honeycomb. As the hyperplane moves through...
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and 12 icosahedra around each vertex, in a regular dodecahedral vertex figure. A geometric honeycomb is a space-filling of polyhedral or higher-dimensional...
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dodecahedral honeycomb Weaire–Phelan structure Convex uniform honeycombs in hyperbolic space Order-4 dodecahedral honeycomb Order-5 cubic honeycomb Order-5...
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Tesseract (redirect from Order-3-3 square honeycomb)
projection of the tesseract into three-dimensional space has a rhombic dodecahedral envelope. Two vertices of the tesseract are projected to the origin....
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Ideal polyhedron (section Honeycombs)
respectively the order-6 tetrahedral honeycomb, order-6 cubic honeycomb, order-4 octahedral honeycomb, and order-6 dodecahedral honeycomb; here the order refers...
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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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The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is...
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600-cell (redirect from Order-5 tetrahedral honeycomb)
5-cell {3,3,3}, 16-cell {3,3,4} of Euclidean 4-space, and the order-6 tetrahedral honeycomb {3,3,6} of hyperbolic space. All of these have tetrahedral cells...
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honeycombs with {p,5,3} Schläfli symbol, and dodecahedral vertex figures: In the geometry of hyperbolic 3-space, the order-5-3 pentagonal honeycomb or...
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120-cell – regular 4-polytope with dodecahedral cells Order-5 dodecahedral honeycomb - regular hyperbolic honeycomb with same Schläfli type, {5,3,5}. (The...
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Rhombic dodecahedron (redirect from Rhombic dodecahedral)
centered cubic (bcc) crystals. Some minerals such as garnet form a rhombic dodecahedral crystal habit. As Johannes Kepler noted in his 1611 book on snowflakes...
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24-cell (redirect from Order-4-3 triangular honeycomb)
in a single 24-cell or its honeycomb. The 24-cell is the fourth in the sequence of 6 convex regular 4-polytopes (in order of size and complexity). It...
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Pentagonal polytope (section Dodecahedral)
(120 dodecahedral cells) Order-3 120-cell honeycomb, {5, 3, 3, 3} (tessellates hyperbolic 4-space (∞ 120-cell facets) The facets of each dodecahedral pentagonal...
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120-cell (redirect from Order-3-3 pentagonal honeycomb)
Schläfli symbol {5,3,3}. It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron...
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