Steric 5-cubes


5-cube

Steric 5-cube


Stericantic 5-cube


Half 5-cube


Steriruncic 5-cube


Steriruncicantic 5-cube

Orthogonal projections in B5 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
Typeuniform polyteron
Schläfli symbol t0,3{3,32,1}
h4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces82
Cells480
Faces720
Edges400
Vertices80
Vertex figure{3,3}-t1{3,3} antiprism
Coxeter groupsD5, [32,1,1]
Propertiesconvex

Alternate names

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]

Related polytopes

Dimensional family of steric n-cubes
n567
[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]
Cantic
figure
Coxeter
=

=

=
Schläfli h4{4,33} h4{4,34} h4{4,35}

Stericantic 5-cube

Stericantic 5-cube
Typeuniform polyteron
Schläfli symbol t0,1,3{3,32,1}
h2,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces82
Cells720
Faces1840
Edges1680
Vertices480
Vertex figure
Coxeter groupsD5, [32,1,1]
Propertiesconvex

Alternate names

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
Typeuniform polyteron
Schläfli symbol t0,2,3{3,32,1}
h3,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces82
Cells560
Faces1280
Edges1120
Vertices320
Vertex figure
Coxeter groupsD5, [32,1,1]
Propertiesconvex

Alternate names

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
Typeuniform polyteron
Schläfli symbol t0,1,2,3{3,32,1}
h2,3,4{4,3,3,3}
Coxeter-Dynkin diagram
4-faces82
Cells720
Faces2080
Edges2400
Vertices960
Vertex figure
Coxeter groupsD5, [32,1,1]
Propertiesconvex

Alternate names

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

External links

This article is issued from Wikipedia - version of the Thursday, April 23, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.