# Steric 5-cubes

| 5-cube | Steric 5-cube | Stericantic 5-cube |
| Half 5-cube | Steriruncic 5-cube | Steriruncicantic 5-cube |
| Orthogonal projections in B$_5$ Coxeter plane |||
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 | t$_{0,3}${3,3$^{2,1}$}h$_4${4,3,3,3} |
| Coxeter-Dynkin diagram | |
| 4-faces | 82 |
| Cells | 480 |
| Faces | 720 |
| Edges | 400 |
| Vertices | 80 |
| Vertex figure | {3,3}-t$_1${3,3} antiprism |
| Coxeter groups | D$_5$, [3$^{2,1,1}$] |
| Properties | convex |

### Alternate names

* Steric penteract, runcinated demipenteract
* Small prismated hemipenteract (siphin) (Jonathan Bowers)$^{:(x3o3o*b3o3x-siphin)}$

### 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 | B$_5$ |
| Graph | |
| Dihedral symmetry | [10/2] |
| Coxeter plane | D$_5$ | D$_4$ |
| Graph | | |
| Dihedral symmetry | [8] | [6] |
| Coxeter plane | D$_3$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [4] | [4] |

### Related polytopes

Dimensional family of steric n-cubes :
| n | 5 | 6 | 7 | 8 |
| [1$^+$,4,3$^{n-2}$] = [3,3$^{n-3,1}$] | [1$^+$,4,3$^3$] = [3,3$^{2,1}$] | [1$^+$,4,3$^4$] = [3,3$^{3,1}$] | [1$^+$,4,3$^5$] = [3,3$^{4,1}$] | [1$^+$,4,3$^6$] = [3,3$^{5,1}$] |
| Steric figure | | | | |
| Coxeter | = | = | = | = |
| Schläfli | h$_4${4,3$^3$} | h$_4${4,3$^4$} | h$_4${4,3$^5$} | h$_4${4,3$^6$} |

## Stericantic 5-cube

Stericantic 5-cube :
| Type | uniform polyteron |
| Schläfli symbol | t$_{0,1,3}${3,3$^{2,1}$}h$_{2,4}${4,3,3,3} |
| Coxeter-Dynkin diagram | |
| 4-faces | 82 |
| Cells | 720 |
| Faces | 1840 |
| Edges | 1680 |
| Vertices | 480 |
| Vertex figure | |
| Coxeter groups | D$_5$, [3$^{2,1,1}$] |
| Properties | convex |

### Alternate names

* Prismatotruncated hemipenteract (pithin) (Jonathan Bowers)$^{:(x3x3o*b3o3x-pithin)}$

### 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 | B$_5$ |
| Graph | |
| Dihedral symmetry | [10/2] |
| Coxeter plane | D$_5$ | D$_4$ |
| Graph | | |
| Dihedral symmetry | [8] | [6] |
| Coxeter plane | D$_3$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [4] | [4] |

## Steriruncic 5-cube

Steriruncic 5-cube :
| Type | uniform polyteron |
| Schläfli symbol | t$_{0,2,3}${3,3$^{2,1}$}h$_{3,4}${4,3,3,3} |
| Coxeter-Dynkin diagram | |
| 4-faces | 82 |
| Cells | 560 |
| Faces | 1280 |
| Edges | 1120 |
| Vertices | 320 |
| Vertex figure | |
| Coxeter groups | D$_5$, [3$^{2,1,1}$] |
| Properties | convex |

### Alternate names

* Prismatorhombated hemipenteract (pirhin) (Jonathan Bowers)$^{:(x3o3o*b3x3x-pirhin)}$

### 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 | B$_5$ |
| Graph | |
| Dihedral symmetry | [10/2] |
| Coxeter plane | D$_5$ | D$_4$ |
| Graph | | |
| Dihedral symmetry | [8] | [6] |
| Coxeter plane | D$_3$ | A$_3$ |
| Graph | | |
| Dihedral symmetry | [4] | [4] |

## Steriruncicantic 5-cube

Steriruncicantic 5-cube :
| Type | uniform polyteron |
| Schläfli symbol | t$_{0,1,2,3}${3,3$^{2,1}$}h$_{2,3,4}${4,3,3,3} |
| Coxeter-Dynkin diagram | |
| 4-faces | 82 |
| Cells | 720 |
| Faces | 2080 |
| Edges | 2400 |
| Vertices | 960 |
| Vertex figure | |
| Coxeter groups | D$_5$, [3$^{2,1,1}$] |
| Properties | convex |

### Alternate names

* Great prismated hemipenteract (giphin) (Jonathan Bowers)$^{:(x3x3o*b3x3x-giphin)}$

### 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 | B$_5$ |
| Graph | |
| Dihedral symmetry | [10/2] |
| Coxeter plane | D$_5$ | D$_4$ |
| Graph | | |
| Dihedral symmetry | [8] | [6] |
| Coxeter plane | D$_3$ | A$_3$ |
| 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 D$_5$ symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.
D5 polytopes :
| h{4,3,3,3} | h$_2${4,3,3,3} | h$_3${4,3,3,3} | h$_4${4,3,3,3} | h$_{2,3}${4,3,3,3} | h$_{2,4}${4,3,3,3} | h$_{3,4}${4,3,3,3} | h$_{2,3,4}${4,3,3,3} |