Stericated 6-orthoplexes

6-cube t12345


6-orthoplex


Stericated 6-orthoplex


Steritruncated 6-orthoplex


Stericantellated 6-orthoplex


Stericantitruncated 6-orthoplex


Steriruncinated 6-orthoplex


Steriruncitruncated 6-orthoplex


Steriruncicantellated 6-orthoplex


Steriruncicantitruncated 6-orthoplex

Orthogonal projections in B6 Coxeter plane

In six-dimensional geometry, a stericated 6-orthoplex is a convex uniform 6-polytope, constructed as a sterication (4th order truncation) of the regular 6-orthoplex.

There are 16 unique sterications for the 6-orthoplex with permutations of truncations, cantellations, and runcinations. Eight are better represented from the stericated 6-cubes. {{-}}

Stericated 6-orthoplex

Stericated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Small cellated hexacontatetrapeton (Acronym: scag) (Jonathan Bowers)

Steritruncated 6-orthoplex

Steritruncated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Cellitruncated hexacontatetrapeton (Acronym: catog) (Jonathan Bowers)

Stericantellated 6-orthoplex

Stericantellated 6-orthoplex

Type

Schläfli symbols

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Cellirhombated hexacontatetrapeton (Acronym: crag) (Jonathan Bowers)

Stericantitruncated 6-orthoplex

Stericantitruncated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Celligreatorhombated hexacontatetrapeton (Acronym: cagorg) (Jonathan Bowers)

Steriruncinated 6-orthoplex

Steriruncinated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Celliprismated hexacontatetrapeton (Acronym: copog) (Jonathan Bowers)

Steriruncitruncated 6-orthoplex

Steriruncitruncated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Celliprismatotruncated hexacontatetrapeton (Acronym: captog) (Jonathan Bowers)

Steriruncicantellated 6-orthoplex

Steriruncicantellated 6-orthoplex

Type

Schläfli symbol

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Celliprismatorhombated hexacontatetrapeton (Acronym: coprag) (Jonathan Bowers)

Steriruncicantitruncated 6-orthoplex

Steriuncicantitruncated 6-orthoplex

Type

Schläfli symbols

Coxeter-Dynkin diagrams

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Great cellated hexacontatetrapeton (Acronym: gocog) (Jonathan Bowers)

Snub 6-demicube

The snub 6-demicube defined as an alternation of the omnitruncated 6-demicube is not uniform, but it can be given Coxeter diagram or and symmetry [32,1,1,1]+ or [4,(3,3,3,3)+], and constructed from 12 snub 5-demicubes, 64 snub 5-simplexes, 60 snub 24-cell antiprisms, 160 3-s{3,4} duoantiprisms, 240 2-sr{3,3} duoantiprisms, and 11520 irregular 5-simplexes filling the gaps at the deleted vertices.

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

6-cube t1235
6-cube t1245
6-cube t125
6-cube t1345
6-cube t135
6-cube t145
6-cube t15
6-cube t5

References

  • H.S.M. Coxeter:
    • H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973
    • Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com,
      • (Paper 22) H.S.M. Coxeter, Regular and Semi-Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10]
      • (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559–591]
      • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
  • Norman Johnson Uniform Polytopes, Manuscript (1991)
    • N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.