Steric 7-cubes
(Redirected from Steritruncated 7-demicube)
 7-demicube      
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 Steric 7-cube 
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 Stericantic 7-cube
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 Steriruncic 7-cube
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 Steriruncicantic 7-cube
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| Orthogonal projections in D7 Coxeter plane | ||
|---|---|---|
In seven-dimensional geometry, a stericated 7-cube (or runcinated 7-demicube) is a convex uniform 7-polytope, being a runcination of the uniform 7-demicube. There are 4 unique runcinations for the 7-demicube including truncation and cantellation.
Steric 7-cube
| Steric 7-cube | |
|---|---|
| Type | uniform 7-polytope |
| Schläfli symbol | t0,3{3,34,1} h4{4,35} |
| Coxeter-Dynkin diagram | 
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| 5-faces | |
| 4-faces | |
| Cells | |
| Faces | |
| Edges | 20160 |
| Vertices | 2240 |
| Vertex figure | |
| Coxeter groups | D7, [34,1,1] |
| Properties | convex |
Cartesian coordinates
The Cartesian coordinates for the vertices of a steric 7-cube centered at the origin are coordinate permutations:
- (±1,±1,±1,±1,±3,±3,±3)
with an odd number of plus signs.
Images
| Coxeter plane |
B7 | D7 | D6 |
|---|---|---|---|
| Graph | 
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| Dihedral symmetry |
[14/2] | [12] | [10] |
| Coxeter plane | D5 | D4 | D3 |
| Graph | 
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| Dihedral symmetry |
[8] | [6] | [4] |
| Coxeter plane |
A5 | A3 | |
| Graph | 
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| |
| Dihedral symmetry |
[6] | [4] |
Related polytopes
| Dimensional family of steric n-cubes | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| n | 5 | 6 | 7 | 8 | |||||||
| [1+,4,3n-2] = [3,3n-3,1] |
[1+,4,33] = [3,32,1] |
[1+,4,34] = [3,33,1] |
[1+,4,35] = [3,34,1] |
[1+,4,36] = [3,35,1] | |||||||
| Steric figure |
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| Coxeter | =
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| Schläfli | h4{4,33} | h4{4,34} | h4{4,35} | h4{4,36} | |||||||
Stericantic 7-cube
Images
| Coxeter plane |
B7 | D7 | D6 |
|---|---|---|---|
| Graph | 
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| Dihedral symmetry |
[14/2] | [12] | [10] |
| Coxeter plane | D5 | D4 | D3 |
| Graph | 
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|
| Dihedral symmetry |
[8] | [6] | [4] |
| Coxeter plane |
A5 | A3 | |
| Graph | 
|
| |
| Dihedral symmetry |
[6] | [4] |
Steriruncic 7-cube
Images
| Coxeter plane |
B7 | D7 | D6 |
|---|---|---|---|
| Graph | 
|
|
|
| Dihedral symmetry |
[14/2] | [12] | [10] |
| Coxeter plane | D5 | D4 | D3 |
| Graph | 
|
|
|
| Dihedral symmetry |
[8] | [6] | [4] |
| Coxeter plane |
A5 | A3 | |
| Graph | 
|
| |
| Dihedral symmetry |
[6] | [4] |
Steriruncicantic 7-cube
Images
| Coxeter plane |
B7 | D7 | D6 |
|---|---|---|---|
| Graph | 
|
|
|
| Dihedral symmetry |
[14/2] | [12] | [10] |
| Coxeter plane | D5 | D4 | D3 |
| Graph | 
|
|
|
| Dihedral symmetry |
[8] | [6] | [4] |
| Coxeter plane |
A5 | A3 | |
| Graph | 
|
| |
| Dihedral symmetry |
[6] | [4] |
Related polytopes
This polytope is based on the 7-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC6 symmetry, and 32 are unique:
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 [1]
- (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. "7D uniform polytopes (polyexa)".
External links
- Weisstein, Eric W. "Hypercube". MathWorld.
- Polytopes of Various Dimensions
- Multi-dimensional Glossary