Order-5 120-cell honeycomb
| Order-5 120-cell honeycomb | |
|---|---|
| (No image) | |
| Type | Hyperbolic regular honeycomb |
| Schläfli symbol | 5,3,3,5 |
| Coxeter diagram |     |
| 4-faces |  5,3,3 |
| Cells |  5,3 |
| Faces |  5 |
| Face figure | 5 |
| Edge figure |  3,5 |
| Vertex figure |  3,3,5 |
| Dual | Self-dual |
| Coxeter group | K4, [5,3,3,5] |
| Properties | Regular |
In the geometry of hyperbolic 4-space, the order-5 120-cell honeycomb is one of five compact regular space-filling tessellations (or honeycombs). With Schläfli symbol 5,3,3,5, it has five 120-cells around each face. It is self-dual.
Contents
1 Related honeycombs
2 Birectified order-5 120-cell honeycomb
3 See also
4 References
Related honeycombs
It is related to the (order-3) 120-cell honeycomb, and order-4 120-cell honeycomb. It is analogous to the order-5 dodecahedral honeycomb and order-5 pentagonal tiling.
Birectified order-5 120-cell honeycomb
The birectified order-5 120-cell honeycomb constructed by all rectified 600-cells, with octahedron and icosahedron cells, and triangle faces with a 5-5 duoprism vertex figure and has extended symmetry [[5,3,3,5]].
See also
- List of regular polytopes
References
Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. .mw-parser-output cite.citationfont-style:inherit.mw-parser-output qquotes:"""""""'""'".mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em
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)
