Omnitruncated 5-cell
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| Omnitruncated 5-cell | |
|---|---|
 Schlegel diagram with the 5 truncated octahedral cells shown. |
|
| Type | Uniform polychoron |
| Cells | 10  (4.6.6)20  (4.4.6) |
| Faces | 150: 90{4}+60{6} |
| Edges | 240 |
| Vertices | 120 |
| Vertex figure | Chiral irregular tetrahedron |
| Coxeter-Dynkin diagram |   |
| Schläfli symbol | t0,1,2,3{3,3,3} |
| Symmetry group | A4, [3,3,3] |
| Properties | convex |
In geometry, the omnitruncated 5-cell is a uniform polychoron.
Contents |
[edit] Alternative names
- Omnitruncated 5-cell
- Omnitruncated pentachoron
- Omnitruncated 4-simplex
- Great prismatodecachoron
- Gippid (Jonathan Bowers: for great prismatodecachoron)
Just as the truncated octahedron is the permutohedron of order 4, the omnitruncated 5-cell is the permutahedron of order 5.[1] The omnitruncated 5-cell is a zonotope, the Minkowski sum of five line segments parallel to the five lines through the origin and the five vertices of the 5-cell.
[edit] Tessellations
The omnitruncated 5-cell can tessellate 4-dimensional space by itself with 3 hypercells around each face. It has Coxeter-Dynkin diagram of 
.[2] Unlike the 3d honeycomb analogy, the bitruncated cubic honeycomb, which has three different Coxeter group Wythoff constructions, this honeycomb has only one such construction.
[edit] Images
 Schlegel diagram, centered on truncated octahedron |
[edit] See also
[edit] External links
- ^ The permutahedron of order 5
- ^ George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) Lists the tessellation as [140 of 143] Great-prismatodecachoric tetracomb (Omnitruncated pentachoric 4d honeycomb)
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