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Revision as of 17:52, 17 August 2010
| Runcitruncated hexateron | ||
 Orthogonal projection in A5 Coxeter plane | ||
| Type | Uniform 5-polytope | |
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | ||
| Vertices | ||
| Schläfli symbol | t0,1,3{3,3,3,3} | |
| Coxeter-Dynkin diagram |   
| |
| Vertex figure | 
| |
| Coxeter group | A5 | |
| Properties | convex, isogonal | |
In five dimensional geometry, runcitruncated hexateron (or runcitruncated 5-simplex) is a uniform 5-polytope.
Coordinates
The coordinates can be made in 6-space, as 180 permutations of:
- (0,0,1,1,2,3)
This construction exists as one of 64 orthant facets of the runcitruncated hexacross.
Related uniform 5-polytopes
The runcitruncated 5-simplex is one of 19 uniform polytera based on the Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored by projection overlap order, red, orange, yellow, green, cyan, blue, purple having progressively more vertices)
| A5 polytopes | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
 t0 |
 t1 |
 t2 |
 t0,1 |
 t0,2 |
 t1,2 |
 t0,3 | |||||
 t1,3 |
 t0,4 |
 t0,1,2 |
t0,1,3 |
 t0,2,3 |
 t1,2,3 |
 t0,1,4 | |||||
 t0,2,4 |
 t0,1,2,3 |
 t0,1,2,4 |
 t0,1,3,4 |
 t0,1,2,3,4 | |||||||
See also
- Other 5-polytopes (regular):
- Hexateron - {3,3,3,3}
- Penteract - {4,3,3,3}
- Pentacross - {3,3,3,4}
References
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- Richard Klitzing 5D quasiregulars, (multi)prisms, non-prismatic Wythoffian polyterons x3x3o3x3o
External links
- Glossary for hyperspace, George Olshevsky.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary
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