“Tesseractic honeycomb honeycomb”的意思、由来-开放百科全书

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Tesseractic honeycomb honeycomb

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Related honeycombs
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Tesseractic honeycomb honeycomb
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Type	Hyperbolic regular honeycomb
Schläfli symbol	{4,3,3,4,3} {4,3,3^1,1,1}
Coxeter diagram	node_1\|4\|node\|3\|node\|3\|node\|4\|node\|3\|node}} {{CDD\|node_1\|4\|node\|3\|node\|splitsplit1\|branch3\|node}} ↔ {{CDD\|node_1\|4\|node\|3\|node	node\|4\|node_g\|3sg\|node_g}} {{CDD\|nodes_10r\|4a4b\|nodes\|split2\|node\|3\|node}}
5-faces	{4,3,3,4}
4-faces	{4,3,3}
Cells	{4,3}
Faces	{4}
Cell figure	{3}
Face figure	{4,3}
Edge figure	{3,4,3}
Vertex figure	{3,3,4,3}
Dual	Order-4 24-cell honeycomb honeycomb
Coxeter group	R}}₅, [3,4,3,3,4]
Properties	Regular

In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs). It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity. With Schläfli symbol {4,3,3,4,3}, it has three tesseractic honeycombs around each cell. It is dual to the order-4 24-cell honeycomb honeycomb.

Related honeycombs

It is related to the regular Euclidean 4-space tesseractic honeycomb, {4,3,3,4}.

It is analogous to the paracompact cubic honeycomb honeycomb, {4,3,4,3}, in 4-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.

References

Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}. (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)
Coxeter, The Beauty of Geometry: Twelve Essays, Dover Publications, 1999 {{ISBN|0-486-40919-8}} (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II,III,IV,V, p212-213)

1 : Honeycombs (geometry)

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Related honeycombs

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