Pentellated 7-orthoplexes

From Wikipedia, the free encyclopedia

In seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex.

More information Orthogonal projections in B6 Coxeter plane ...
Orthogonal projections in B6 Coxeter plane

7-orthoplex
Pentellated 7-orthoplex
Pentitruncated 7-orthoplex
Penticantellated 7-orthoplex

Penticantitruncated 7-orthoplex
Pentiruncinated 7-orthoplex
Pentiruncitruncated 7-orthoplex
Pentiruncicantellated 7-orthoplex

Pentiruncicantitruncated 7-orthoplex
Pentistericated 7-orthoplex
Pentisteritruncated 7-orthoplex
Pentistericantellated 7-orthoplex

Pentistericantitruncated 7-orthoplex
Pentisteriruncinated 7-orthoplex
Pentisteriruncitruncated 7-orthoplex
Pentisteriruncicantellated 7-orthoplex

Pentisteriruncicantitruncated 7-orthoplex
Close

There are 32 unique pentellations of the 7-orthoplex with permutations of truncations, cantellations, runcinations, and sterications. 16 are more simply constructed relative to the 7-cube.

These polytopes are a part of a set of 127 uniform 7-polytopes with B7 symmetry.

Pentellated 7-orthoplex

Pentellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges20160
Vertices2688
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex

Alternate names

  • Small terated hecatonicosaoctaexon (acronym: Staz) (Jonathan Bowers)[1]

Coordinates

Coordinates are permutations of (0,1,1,1,1,1,2)√2

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentitruncated 7-orthoplex

More information Pentitruncated 7-orthoplex ...
Pentitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges87360
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Teritruncated hecatonicosaoctaexon (acronym: Tetaz) (Jonathan Bowers)[2]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Coordinates

Coordinates are permutations of (0,1,1,1,1,2,3).

Penticantellated 7-orthoplex

More information Penticantellated 7-orthoplex ...
Penticantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,2,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges188160
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Terirhombated hecatonicosaoctaexon (acronym: Teroz) (Jonathan Bowers)[3]

Coordinates

Coordinates are permutations of (0,1,1,1,2,2,3)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Penticantitruncated 7-orthoplex

More information Penticantitruncated 7-orthoplex ...
Penticantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,2,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges295680
Vertices53760
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Terigreatorhombated hecatonicosaoctaexon (acronym: Tograz) (Jonathan Bowers)[4]

Coordinates

Coordinates are permutations of (0,1,1,1,2,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentiruncinated 7-orthoplex

More information Pentiruncinated 7-orthoplex ...
Pentiruncinated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges174720
Vertices26880
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Teriprismated hecatonicosaoctaexon (acronym: Topaz) (Jonathan Bowers)[5]

Coordinates

The coordinates are permutations of (0,1,1,2,2,2,3)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentiruncitruncated 7-orthoplex

More information Pentiruncitruncated 7-orthoplex ...
Pentiruncitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges443520
Vertices80640
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Teriprismatotruncated hecatonicosaoctaexon (acronym: Toptaz) (Jonathan Bowers)[6]

Coordinates

Coordinates are permutations of (0,1,1,2,2,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentiruncicantellated 7-orthoplex

More information Pentiruncicantellated 7-orthoplex ...
Pentiruncicantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,2,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges403200
Vertices80640
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Teriprismatorhombated hecatonicosaoctaexon (acronym: Toparz) (Jonathan Bowers)[7]

Coordinates

Coordinates are permutations of (0,1,1,2,3,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentiruncicantitruncated 7-orthoplex

More information Pentiruncicantitruncated 7-orthoplex ...
Pentiruncicantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges725760
Vertices161280
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Terigreatoprismated hecatonicosaoctaexon (acronym: Tegopaz) (Jonathan Bowers)[8]

Coordinates

Coordinates are permutations of (0,1,1,2,3,4,5)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentistericated 7-orthoplex

More information Pentistericated 7-orthoplex ...
Pentistericated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges67200
Vertices13440
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Tericellated hecatonicosaoctaexon (acronym: Tocaz) (Jonathan Bowers)[9]

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Coordinates

Coordinates are permutations of (0,1,2,2,2,2,3)√2.

Pentisteritruncated 7-orthoplex

More information Pentisteritruncated 7-orthoplex ...
Pentisteritruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges241920
Vertices53760
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Tericellitruncated hecatonicosaoctaexon (acronym: Tacotaz) (Jonathan Bowers)[10]

Coordinates

Coordinates are permutations of (0,1,2,2,2,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentistericantellated 7-orthoplex

More information Pentistericantellated 7-orthoplex ...
Pentistericantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,2,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges403200
Vertices80640
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Tericellirhombated hecatonicosaoctaexon (acronym: Tocarz) (Jonathan Bowers)[11]

Coordinates

Coordinates are permutations of (0,1,2,2,3,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentistericantitruncated 7-orthoplex

More information Pentistericantitruncated 7-orthoplex ...
Pentistericantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,2,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges645120
Vertices161280
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Tericelligreatorhombated hecatonicosaoctaexon (acronym: Tecagraz) (Jonathan Bowers)[12]

Coordinates

Coordinates are permutations of (0,1,2,2,3,4,5)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentisteriruncinated 7-orthoplex

More information Pentisteriruncinated 7-orthoplex ...
Pentisteriruncinated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges241920
Vertices53760
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bipenticantitruncated 7-orthoplex as t1,2,3,6{35,4}
  • Tericelliprismated hecatonicosaoctaexon (acronym: Tecpaz) (Jonathan Bowers)[13]

Coordinates

Coordinates are permutations of (0,1,2,3,3,3,4)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentisteriruncitruncated 7-orthoplex

More information Pentisteriruncitruncated 7-orthoplex ...
Pentisteriruncitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges645120
Vertices161280
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Tericelliprismatotruncated hecatonicosaoctaexon (acronym: Tecpotaz) (Jonathan Bowers)[14]

Coordinates

Coordinates are permutations of (0,1,2,3,3,4,5)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentisteriruncicantellated 7-orthoplex

More information Pentisteriruncicantellated 7-orthoplex ...
Pentisteriruncicantellated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,2,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges645120
Vertices161280
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Bipentiruncicantitruncated 7-orthoplex as t1,2,3,4,6{35,4}
  • Tericelliprismatorhombated hecatonicosaoctaexon (acronym: Tacparez) (Jonathan Bowers)[15]

Coordinates

Coordinates are permutations of (0,1,2,3,4,4,5)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Pentisteriruncicantitruncated 7-orthoplex

More information Pentisteriruncicantitruncated 7-orthoplex ...
Pentisteriruncicantitruncated 7-orthoplex
Typeuniform 7-polytope
Schläfli symbolt0,1,2,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges1128960
Vertices322560
Vertex figure
Coxeter groupsB7, [4,35]
Propertiesconvex
Close

Alternate names

  • Great terated hecatonicosaoctaexon (acronym: Gotaz) (Jonathan Bowers)[16]

Coordinates

Coordinates are permutations of (0,1,2,3,4,5,6)√2.

Images

More information Coxeter plane, B7 / A6 ...
Orthographic projections
Coxeter plane B7 / A6 B6 / D7 B5 / D6 / A4
Graph too complex
Dihedral symmetry [14] [12] [10]
Coxeter plane B4 / D5 B3 / D4 / A2 B2 / D3
Graph
Dihedral symmetry [8] [6] [4]
Coxeter plane A5 A3
Graph
Dihedral symmetry [6] [4]
Close

Notes

References

External links

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