# Steric 5-cubes

(Redirected from Steriruncic 5-cube)
 Orthogonal projections in B5 Coxeter plane 5-cube Steric 5-cube Stericantic 5-cube Half 5-cube Steriruncic 5-cube Steriruncicantic 5-cube

In five-dimensional geometry, a steric 5-cube or (steric 5-demicube or sterihalf 5-cube) is a convex uniform 5-polytope. There are unique 4 steric forms of the 5-cube. Steric 5-cubes have half the vertices of stericated 5-cubes.

## Steric 5-cube

Steric 5-cube
Type uniform polyteron
Schläfli symbol t0,3{3,32,1}
h4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 82
Cells 480
Faces 720
Edges 400
Vertices 80
Vertex figure {3,3}-t1{3,3} antiprism
Coxeter groups D5, [32,1,1]
Properties convex

### Alternate names

• Steric penteract, runcinated demipenteract
• Small prismated hemipenteract (siphin) (Jonathan Bowers)[1]

### Cartesian coordinates

The Cartesian coordinates for the 80 vertices of a steric 5-cube centered at the origin are the permutations of

(±1,±1,±1,±1,±3)

with an odd number of plus signs.

### Images

orthographic projections
Coxeter plane B5
Graph
Dihedral symmetry [10/2]
Coxeter plane D5 D4
Graph
Dihedral symmetry [8] [6]
Coxeter plane D3 A3
Graph
Dihedral symmetry [4] [4]

## Stericantic 5-cube

Stericantic 5-cube
Type uniform polyteron
Schläfli symbol t0,1,3{3,32,1}
h2,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 82
Cells 720
Faces 1840
Edges 1680
Vertices 480
Vertex figure
Coxeter groups D5, [32,1,1]
Properties convex

### Alternate names

• Prismatotruncated hemipenteract (pithin) (Jonathan Bowers)[2]

### Cartesian coordinates

The Cartesian coordinates for the 480 vertices of a stericantic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±3,±3,±5)

with an odd number of plus signs.

### Images

orthographic projections
Coxeter plane B5
Graph
Dihedral symmetry [10/2]
Coxeter plane D5 D4
Graph
Dihedral symmetry [8] [6]
Coxeter plane D3 A3
Graph
Dihedral symmetry [4] [4]

## Steriruncic 5-cube

Steriruncic 5-cube
Type uniform polyteron
Schläfli symbol t0,2,3{3,32,1}
h3,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 82
Cells 560
Faces 1280
Edges 1120
Vertices 320
Vertex figure
Coxeter groups D5, [32,1,1]
Properties convex

### Alternate names

• Prismatorhombated hemipenteract (pirhin) (Jonathan Bowers)[3]

### Cartesian coordinates

The Cartesian coordinates for the 320 vertices of a steriruncic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±5)

with an odd number of plus signs.

### Images

orthographic projections
Coxeter plane B5
Graph
Dihedral symmetry [10/2]
Coxeter plane D5 D4
Graph
Dihedral symmetry [8] [6]
Coxeter plane D3 A3
Graph
Dihedral symmetry [4] [4]

## Steriruncicantic 5-cube

Steriruncicantic 5-cube
Type uniform polyteron
Schläfli symbol t0,1,2,3{3,32,1}
h2,3,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces 82
Cells 720
Faces 2080
Edges 2400
Vertices 960
Vertex figure
Coxeter groups D5, [32,1,1]
Properties convex

### Alternate names

• Great prismated hemipenteract (giphin) (Jonathan Bowers)[4]

### Cartesian coordinates

The Cartesian coordinates for the 960 vertices of a steriruncicantic 5-cube centered at the origin are coordinate permutations:

(±1,±1,±3,±5,±7)

with an odd number of plus signs.

### Images

orthographic projections
Coxeter plane B5
Graph
Dihedral symmetry [10/2]
Coxeter plane D5 D4
Graph
Dihedral symmetry [8] [6]
Coxeter plane D3 A3
Graph
Dihedral symmetry [4] [4]

## Related polytopes

This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 23 uniform polytera (uniform 5-polytope) that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.

## Notes

1. ^ Klitzing, (x3o3o *b3o3x - siphin)
2. ^ Klitzing, (x3x3o *b3o3x - pithin)
3. ^ Klitzing, (x3o3o *b3x3x - pirhin)
4. ^ Klitzing, (x3x3o *b3x3x - giphin)

## 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. "5D uniform polytopes (polytera)". x3o3o *b3o3x - siphin, x3x3o *b3o3x - pithin, x3o3o *b3x3x - pirhin, x3x3o *b3x3x - giphin