Orthogonal projections in B6 Coxeter plane | |||
---|---|---|---|
6-orthoplex |
Pentellated 6-orthoplex Pentellated 6-cube |
6-cube |
Pentitruncated 6-orthoplex |
Penticantellated 6-orthoplex |
Penticantitruncated 6-orthoplex |
Pentiruncitruncated 6-orthoplex |
Pentiruncicantellated 6-cube |
Pentiruncicantitruncated 6-orthoplex |
Pentisteritruncated 6-cube |
Pentistericantitruncated 6-orthoplex |
Pentisteriruncicantitruncated 6-orthoplex (Omnitruncated 6-cube) |
In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex.
There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. Ten are shown, with the other 6 more easily constructed as a pentellated 6-cube. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex, constructed by an expansion operation applied to the regular 6-orthoplex. The highest form, the pentisteriruncicantitruncated 6-orthoplex, is called an omnitruncated 6-orthoplex with all of the nodes ringed.
Pentitruncated 6-orthoplex
Pentitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 8640 |
Vertices | 1920 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Teritruncated hexacontatetrapeton (Acronym: tacox) (Jonathan Bowers)[1]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Penticantellated 6-orthoplex
Penticantellated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,2,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 21120 |
Vertices | 3840 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Terirhombated hexacontitetrapeton (Acronym: tapox) (Jonathan Bowers)[2]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Penticantitruncated 6-orthoplex
Penticantitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 30720 |
Vertices | 7680 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Terigreatorhombated hexacontitetrapeton (Acronym: togrig) (Jonathan Bowers)[3]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Pentiruncitruncated 6-orthoplex
Pentiruncitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,3,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 51840 |
Vertices | 11520 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Teriprismatotruncated hexacontitetrapeton (Acronym: tocrax) (Jonathan Bowers)[4]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Pentiruncicantitruncated 6-orthoplex
Pentiruncicantitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,3,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 80640 |
Vertices | 23040 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Terigreatoprismated hexacontitetrapeton (Acronym: tagpog) (Jonathan Bowers)[5]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Pentistericantitruncated 6-orthoplex
Pentistericantitruncated 6-orthoplex | |
---|---|
Type | uniform 6-polytope |
Schläfli symbol | t0,1,2,4,5{3,3,3,3,4} |
Coxeter-Dynkin diagrams | |
5-faces | |
4-faces | |
Cells | |
Faces | |
Edges | 80640 |
Vertices | 23040 |
Vertex figure | |
Coxeter groups | B6, [4,3,3,3,3] |
Properties | convex |
Alternate names
- Tericelligreatorhombated hexacontitetrapeton (Acronym: tecagorg) (Jonathan Bowers)[6]
Images
Coxeter plane | B6 | B5 | B4 |
---|---|---|---|
Graph | |||
Dihedral symmetry | [12] | [10] | [8] |
Coxeter plane | B3 | B2 | |
Graph | |||
Dihedral symmetry | [6] | [4] | |
Coxeter plane | A5 | A3 | |
Graph | |||
Dihedral symmetry | [6] | [4] |
Related polytopes
These polytopes are from a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.
Notes
References
- H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- 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
- (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
- (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
- Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
- Klitzing, Richard. "6D uniform polytopes (polypeta)". x4o3o3o3x3x - tacox, x4o3o3x3o3x - tapox, x4o3o3x3x3x - togrig, x4o3x3o3x3x - tocrax, x4x3o3x3x3x - tagpog, x4x3o3x3x3x - tecagorg
External links
- Glossary for hyperspace, George Olshevsky.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary