Pentellated 6-orthoplex

Orthogonal projections in BC6 Coxeter plane

6-orthoplex

Pentellated 6-orthoplex
Pentellated 6-cube

6-cube

Pentitruncated 6-orthoplex

Penticantellated 6-orthoplex

Penticantitruncated 6-orthoplex

Pentiruncitruncated 6-orthoplex

Pentiruncicantellated 6-cube

Pentiruncicantitruncated 6-orthoplex

Pentisteritruncated 6-cube

Pentistericantitruncated 6-orthoplex

Pentisteriruncicantitruncated 6-orthoplex
(Omnitruncated 6-cube)

In six-dimensional geometry, a pentellated 6-orthoplex is a convex uniform 6-polytope with 5th order truncations of the regular 6-orthoplex.

There are unique 16 degrees of pentellations of the 6-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. Ten are shown, with the other 6 more easily constructed as a pentellated 6-cube. The simple pentellated 6-orthoplex (Same as pentellated 5-cube) is also called an expanded 6-orthoplex, constructed by an expansion operation applied to the regular 6-orthoplex. The highest form, the pentisteriruncicantitruncated 6-orthoplex, is called an omnitruncated 6-orthoplex with all of the nodes ringed.

Contents

Pentitruncated 6-orthoplex

Pentitruncated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,1,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 8640
Vertices 1920
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Penticantellated 6-orthoplex

Penticantellated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,2,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 21120
Vertices 3840
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Penticantitruncated 6-orthoplex

Penticantitruncated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,1,2,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 30720
Vertices 7680
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Pentiruncitruncated 6-orthoplex

Pentiruncitruncated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,1,3,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 51840
Vertices 11520
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Pentiruncicantitruncated 6-orthoplex

Pentiruncicantitruncated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,1,2,3,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 23040
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Pentistericantitruncated 6-orthoplex

Pentistericantitruncated 6-orthoplex
Type uniform polypeton
Schläfli symbol t0,1,2,4,5{3,3,3,3,4}
Coxeter-Dynkin diagrams
5-faces
4-faces
Cells
Faces
Edges 80640
Vertices 23040
Vertex figure
Coxeter groups BC6, [4,3,3,3,3]
Properties convex

Alternate names

Images

orthographic projections
Coxeter plane B6 B5 B4
Graph
Dihedral symmetry [12] [10] [8]
Coxeter plane B3 B2
Graph
Dihedral symmetry [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]

Related polytopes

These polytopes are from a set of 63 uniform polypeta generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex.


β6

t1β6

t2β6

t2γ6

t1γ6

γ6

t0,1β6

t0,2β6

t1,2β6

t0,3β6

t1,3β6

t2,3γ6

t0,4β6

t1,4γ6

t1,3γ6

t1,2γ6

t0,5γ6

t0,4γ6

t0,3γ6

t0,2γ6

t0,1γ6

t0,1,2β6

t0,1,3β6

t0,2,3β6

t1,2,3β6

t0,1,4β6

t0,2,4β6

t1,2,4β6

t0,3,4β6

t1,2,4γ6

t1,2,3γ6

t0,1,5β6

t0,2,5β6

t0,3,4γ6

t0,2,5γ6

t0,2,4γ6

t0,2,3γ6

t0,1,5γ6

t0,1,4γ6

t0,1,3γ6

t0,1,2γ6

t0,1,2,3β6

t0,1,2,4β6

t0,1,3,4β6

t0,2,3,4β6

t1,2,3,4γ6

t0,1,2,5β6

t0,1,3,5β6

t0,2,3,5γ6

t0,2,3,4γ6

t0,1,4,5γ6

t0,1,3,5γ6

t0,1,3,4γ6

t0,1,2,5γ6

t0,1,2,4γ6

t0,1,2,3γ6

t0,1,2,3,4β6

t0,1,2,3,5β6

t0,1,2,4,5β6

t0,1,2,4,5γ6

t0,1,2,3,5γ6

t0,1,2,3,4γ6

t0,1,2,3,4,5γ6

Notes

  1. ^ Klitzing, (x4o3o3o3x3x - tacox)
  2. ^ Klitzing, (x4o3o3x3o3x - tapox)
  3. ^ Klitzing, (x4o3o3x3x3x - togrig)
  4. ^ Klitzing, (x4o3x3o3x3x - tocrax)
  5. ^ Klitzing, (x4x3o3x3x3x - tagpog)
  6. ^ Klitzing, (x4x3o3x3x3x - tecagorg)

References

External links