Steric 7-cubes

160px
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

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.

## Contents

* 1 Steric 7-cube
* 1.1 Cartesian coordinates
* 1.2 Images
* 1.3 Related polytopes
* 2 Stericantic 7-cube
* 2.1 Images
* 3 Steriruncic 7-cube
* 3.1 Images
* 4 Steriruncicantic 7-cube
* 4.1 Images
* 5 Related polytopes
* 6 Notes
* 7 References
* 8 External links

## Steric 7-cube

Steric 7-cube

Type | uniform 7-polytope
Schläfli symbol | t0,3{3,34,1}
h4{4,35}
Coxeter-Dynkin diagram |

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

Template:7-demicube Coxeter plane graphs

### Related polytopes

Template:Steric cube table

## Stericantic 7-cube

### Images

Template:7-demicube Coxeter plane graphs

## Steriruncic 7-cube

### Images

Template:7-demicube Coxeter plane graphs

## Steriruncicantic 7-cube

### Images

Template:7-demicube Coxeter plane graphs

## 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: Template:Demihepteract family

## 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)". https://bendwavy.org/klitzing/dimensions/polyexa.htm.

## External links

* Weisstein, Eric W.. "Hypercube". http://mathworld.wolfram.com/Hypercube.html.
* Polytopes of Various Dimensions
* Multi-dimensional Glossary

* v
* t
* e

Fundamental convex regular and uniform polytopes in dimensions 2–10

Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn
Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube |  | Dodecahedron • Icosahedron
Uniform 4-polytope | 5-cell | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube |  |
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 |
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 |
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 |
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube |  |
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube |  |
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds

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