Cantellated 6-demicube


6-cube

Cantellated 6-demicube

Cantitruncated 6-demicube
Orthogonal projections in D6 Coxeter plane

In six-dimensional geometry, a cantellated 6-demicube is a convex uniform 6-polytope, being a cantellation of the uniform 6-demicube. There are 2 unique cantellation for the 6-demicube including a truncation.

Contents


Cantellated 6-demicube

Cantellated 6-demicube
Type uniform polypeton
Schläfli symbol t0,2{3,33,1}
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges 3840
Vertices 640
Vertex figure
Coxeter groups D6, [33,1,1]
Properties convex

Alternate names

Cartesian coordinates

The Cartesian coordinates for the vertices of a cantellated demihexeract centered at the origin are coordinate permutations:

(±1,±1,±1,±1,±3,±3)

with an odd number of plus signs.

Images

orthographic projections
Coxeter plane B6
Graph
Dihedral symmetry [12/2]
Coxeter plane D6 D5
Graph
Dihedral symmetry [10] [8]
Coxeter plane D4 D3
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Cantitruncated 6-demicube

Cantitruncated 6-demicube
Type uniform polypeton
Schläfli symbol t0,1,2{3,33,1}
Coxeter-Dynkin diagram
5-faces
4-faces
Cells
Faces
Edges 5760
Vertices 1920
Vertex figure
Coxeter groups D6, [33,1,1]
Properties convex

Alternate names

Cartesian coordinates

The Cartesian coordinates for the vertices of a cantitruncated demihexeract centered at the origin are coordinate permutations:

(±1,±1,±1,±3,±5,±5)

with an odd number of plus signs.

Images

orthographic projections
Coxeter plane B6
Graph
Dihedral symmetry [12/2]
Coxeter plane D6 D5
Graph
Dihedral symmetry [10] [8]
Coxeter plane D4 D3
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Related polytopes

This polytope is based on the 6-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:


t0(131)

t0,1(131)

t0,2(131)

t0,3(131)

t0,4(131)

t0,1,2(131)

t0,1,3(131)

t0,1,4(131)

t0,2,3(131)

t0,2,4(131)

t0,3,4(131)

t0,1,2,3(131)

t0,1,2,4(131)

t0,1,3,4(131)

t0,2,3,4(131)

t0,1,2,3,4(131)

Notes

  1. ^ Klitzing, (x3o3o *b3x3o3o - sirhax)
  2. ^ Klitzing, (x3x3o *b3x3o3o - girhax)

References

External links