Truncated 5-cell honeycomb
| Truncated 4-simplex honeycomb | |
|---|---|
| (No image) | |
| Type | Uniform honeycomb |
| Family | Truncated simplectic honeycomb |
| Schläfli symbol | t0,1{3[5]} |
| Coxeter–Dynkin diagrams | |
| 4-face types | {3,3,3} t0,1{3,3,3} |
| Cell types | {3,3} t0,1{3,3} |
| Face types | Triangle {3} Hexagon {6} |
| Vertex figure | Elongated tetrahedral antiprism |
| Coxeter groups |  , [3[5]] |
| Properties | vertex-transitive |
In four-dimensional Euclidean geometry, the truncated 4-simplex honeycomb, truncated 5-cell honeycomb is a space-filling tessellation honeycomb. It is composed of 5-cells, truncated 5-cells, and bitruncated 5-cells facets in a ratio of 2:2:1.
Parallel cells of this honeycomb can be grouped into 5 sets of parallel hyperplanes, each filled by a quarter cubic honeycomb.[1]
Contents |
Alternate names
- Cyclotruncated pentachoric tetracomb
- Small truncated-pentachoric tetracomb
Related polytopes and honeycombs
This honeycomb is one of 7 unique uniform honycombs constructed by the Coxeter group. The other 6 have Coxeter–Dynkin diagrams as: , , , ,, .
See also
- Regular and uniform honeycombs in 4-space:
Notes
- ^ Olshevsky, 2006 (Model 135)
References
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 135
- Richard Klitzing, 4D, Euclidean tesselations, x3x3x3x3x3*a - otcypit - 135