Order-4 24-cell honeycomb
In the geometry of hyperbolic 4-space, the order-4 24-cell honeycomb is one of two 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 {3,4,3,4}, it has four 24-cells around each face. It is dual to the cubic honeycomb honeycomb.
| Order-4 24-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | {3,4,3,4} {3,4,31,1} |
| Coxeter diagram |        |
| 4-faces |  |
| Cells |  |
| Faces |  |
| Face figure |  |
| Edge figure | |
| Vertex figure |  |
| Dual | Cubic honeycomb honeycomb |
| Coxeter group | R4, [4,3,4,3] |
| Properties | Regular |
Related honeycombs
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, with 24-cell facets.
gollark: You *can*, but loading all the information - much of it conflicting - into your brain *has* been known to lead to a few moderately problematic side effects.
gollark: Now, while modern mindstate execution is fully deterministic, people aren't perfect judges of the "best" thing and there's some noise, so you probably want to use comparison counting sort or something.
gollark: You can either read aesthetic appreciation data out of their mindstates and rank that, or just use one per *comparison* instead.
gollark: We use a few countable infinities of them as workers, although some need the existential horror neural pathways damped a lot.
gollark: Happily, this also avoids issues with ordering effects.
See also
- List of regular polytopes
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)
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