Pentellated 7-cubes
In seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There are 32 unique of the 7-cube with permutations of truncations, cantellations, runcinations, and . 16 are more simply constructed relative to the 7-orthoplex.
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Pentellated 7-cube
Pentellated 7-cube |
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Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Small hepteract (acronym: stesa) (Jonathan Bowers)
Pentitruncated 7-cube
Pentitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Teritruncated hepteract (acronym: tetsa) (Jonathan Bowers)
Penticantellated 7-cube
Penticantellated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Terirhombated hepteract (acronym: tersa) (Jonathan Bowers)
Penticantitruncated 7-cube
Penticantitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Terigreatorhombated hepteract (acronym: togresa) (Jonathan Bowers)
Pentiruncinated 7-cube
Pentiruncinated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Teriprismated hepteract (acronym: tapsa) (Jonathan Bowers)
Pentiruncitruncated 7-cube
Pentiruncitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Teriprismatotruncated hepteract (acronym: toptosa) (Jonathan Bowers)
Pentiruncicantellated 7-cube
Pentiruncicantellated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Teriprismatorhombated hepteract (acronym: topresa) (Jonathan Bowers)
Pentiruncicantitruncated 7-cube
Pentiruncicantitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Terigreatoprismated hepteract (acronym: togapsa) (Jonathan Bowers)
Pentistericated 7-cube
Pentistericated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Tericellated hepteract (acronym: tacosa) (Jonathan Bowers)
Pentisteritruncated 7-cube
Pentisteritruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Tericellitruncated hepteract (acronym: tecatsa) (Jonathan Bowers)
Pentistericantellated 7-cube
Pentistericantellated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Tericellirhombated hepteract (acronym: tecresa) (Jonathan Bowers)
Pentistericantitruncated 7-cube
Pentistericantitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Tericelligreatorhombated hepteract (acronym: tecgresa) (Jonathan Bowers)
Pentisteriruncinated 7-cube
Pentisteriruncinated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Bipenticantitruncated 7-cube as t1,2,3,6{4,35}
- Tericelliprismated hepteract (acronym: tecpasa) (Jonathan Bowers)
Pentisteriruncitruncated 7-cube
Pentisteriruncitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Tericelliprismatotruncated hepteract (acronym: tecpetsa) (Jonathan Bowers)
Pentisteriruncicantellated 7-cube
Pentisteriruncicantellated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Bipentiruncicantitruncated 7-cube as t1,2,3,4,6{4,35}
- Tericelliprismatorhombated hepteract (acronym: tocpresa) (Jonathan Bowers)
Pentisteriruncicantitruncated 7-cube
Pentisteriruncicantitruncated 7-cube |
|---|
Type |
Schläfli symbol |
Coxeter-Dynkin diagrams |
6-faces |
5-faces |
4-faces |
Cells |
Faces |
Edges |
Vertices |
Vertex figure |
Coxeter groups |
Properties |
Alternate names
- Great hepteract (acronym: gotesa) (Jonathan Bowers)
Related polytopes
These polytopes are a part of a set of 127 uniform 7-polytopes with B7 symmetry.
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 Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com,
- (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.