Cantic 5-cube

Truncated 5-demicube
Cantic 5-cube

D5 Coxeter plane projection
Typeuniform 5-polytope
Schläfli symbol h2{4,3,3,3}
t{3,32,1}
Coxeter-Dynkin diagram =
4-faces42 total:
16 r{3,3,3}
16 t{3,3,3}
10 t{3,3,4}
Cells280 total:
80 {3,3}
120 t{3,3}
80 {3,4}
Faces640 total:
480 {3}
160 {6}
Edges560
Vertices160
Vertex figure
Triangular prism pyramid
Coxeter groupsD5, [32,1,1]
Propertiesconvex

In geometry of five dimensions or higher, a cantic 5-cube, cantihalf 5-cube, truncated 5-demicube is a uniform 5-polytope, being a truncation of the 5-demicube. It has half the vertices of a cantellated 5-cube.

Cartesian coordinates

The Cartesian coordinates for the 160 vertices of a cantic 5-cube centered at the origin and edge length 6√2 are coordinate permutations:

(±1,±1,±3,±3,±3)

with an odd number of plus signs.

Alternate names

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

It has half the vertices of the cantellated 5-cube, as compared here in the B5 Coxeter plane projections:


Cantic 5-cube
Cantellated 5-cube

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.

Dimensional family of cantic n-cubes
n345678
Symmetry
[1+,4,3n-2]		 [1+,4,3]
= [3,3]		 [1+,4,32]
= [3,31,1]		 [1+,4,33]
= [3,32,1]		 [1+,4,34]
= [3,33,1]		 [1+,4,35]
= [3,34,1]		 [1+,4,36]
= [3,35,1]
Cantic
figure
Coxeter
=
=
=
=
=
=
Schläfli h2{4,3} h2{4,32} h2{4,33} h2{4,34} h2{4,35} h2{4,36}

There are 23 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, (x3x3o *b3o3o - thin)

References

External links

Fundamental convex regular and uniform polytopes in dimensions 2–10
Family An Bn I2(p) / Dn E6 / E7 / E8 / E9 / E10 / 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
This article is issued from Wikipedia - version of the 4/23/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.