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Contents

   



(Top)
  


1 Pentellated 7-orthoplex  


1.1  Alternate names  




1.2  Coordinates  




1.3  Images  






2 Pentitruncated 7-orthoplex  


2.1  Alternate names  




2.2  Images  




2.3  Coordinates  






3 Penticantellated 7-orthoplex  


3.1  Alternate names  




3.2  Coordinates  




3.3  Images  






4 Penticantitruncated 7-orthoplex  


4.1  Alternate names  




4.2  Coordinates  






5 Pentiruncinated 7-orthoplex  


5.1  Alternate names  




5.2  Coordinates  




5.3  Images  






6 Pentiruncitruncated 7-orthoplex  


6.1  Alternate names  




6.2  Coordinates  




6.3  Images  






7 Pentiruncicantellated 7-orthoplex  


7.1  Alternate names  




7.2  Coordinates  




7.3  Images  






8 Pentiruncicantitruncated 7-orthoplex  


8.1  Alternate names  




8.2  Coordinates  




8.3  Images  






9 Pentistericated 7-orthoplex  


9.1  Alternate names  




9.2  Images  




9.3  Coordinates  






10 Pentisteritruncated 7-orthoplex  


10.1  Alternate names  




10.2  Coordinates  




10.3  Images  






11 Pentistericantellated 7-orthoplex  


11.1  Alternate names  




11.2  Coordinates  




11.3  Images  






12 Pentistericantitruncated 7-orthoplex  


12.1  Alternate names  




12.2  Coordinates  




12.3  Images  






13 Pentisteriruncinated 7-orthoplex  


13.1  Alternate names  




13.2  Coordinates  




13.3  Images  






14 Pentisteriruncitruncated 7-orthoplex  


14.1  Alternate names  




14.2  Coordinates  




14.3  Images  






15 Pentisteriruncicantellated 7-orthoplex  


15.1  Alternate names  




15.2  Coordinates  




15.3  Images  






16 Pentisteriruncicantitruncated 7-orthoplex  


16.1  Alternate names  




16.2  Coordinates  




16.3  Images  






17 Notes  




18 References  




19 External links  













Pentellated 7-orthoplexes







Add links
  








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From Wikipedia, the free encyclopedia
  
(Redirected from Pentellated 7-orthoplex)
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

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

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[edit]

Pentellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 20160
Vertices 2688
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentitruncated 7-orthoplex[edit]

pentitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 87360
Vertices 13440
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Images[edit]

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]

Coordinates[edit]

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

Penticantellated 7-orthoplex[edit]

Penticantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 188160
Vertices 26880
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Penticantitruncated 7-orthoplex[edit]

penticantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 295680
Vertices 53760
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

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]

Pentiruncinated 7-orthoplex[edit]

pentiruncinated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 174720
Vertices 26880
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentiruncitruncated 7-orthoplex[edit]

pentiruncitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 443520
Vertices 80640
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentiruncicantellated 7-orthoplex[edit]

pentiruncicantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 403200
Vertices 80640
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentiruncicantitruncated 7-orthoplex[edit]

pentiruncicantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 725760
Vertices 161280
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentistericated 7-orthoplex[edit]

pentistericated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 67200
Vertices 13440
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Images[edit]

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]

Coordinates[edit]

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

Pentisteritruncated 7-orthoplex[edit]

pentisteritruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 241920
Vertices 53760
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentistericantellated 7-orthoplex[edit]

pentistericantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 403200
Vertices 80640
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentistericantitruncated 7-orthoplex[edit]

pentistericantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 645120
Vertices 161280
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentisteriruncinated 7-orthoplex[edit]

Pentisteriruncinated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 241920
Vertices 53760
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentisteriruncitruncated 7-orthoplex[edit]

pentisteriruncitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 645120
Vertices 161280
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentisteriruncicantellated 7-orthoplex[edit]

pentisteriruncicantellated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,2,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 645120
Vertices 161280
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Pentisteriruncicantitruncated 7-orthoplex[edit]

pentisteriruncicantitruncated 7-orthoplex
Type uniform 7-polytope
Schläfli symbol t0,1,2,3,4,5{35,4}
Coxeter diagram
6-faces
5-faces
4-faces
Cells
Faces
Edges 1128960
Vertices 322560
Vertex figure
Coxeter groups B7, [4,35]
Properties convex

Alternate names[edit]

Coordinates[edit]

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

Images[edit]

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]

Notes[edit]

  1. ^ Klitzing, (x3o3o3o3o3x4o - )
  • ^ Klitzing, (x3x3o3o3o3x4o - )
  • ^ Klitzing, (x3o3x3o3o3x4o - )
  • ^ Klitzing, (x3x3x3oxo3x4o - )
  • ^ Klitzing, (x3o3o3x3o3x4o - )
  • ^ Klitzing, (x3x3o3x3o3x4o - )
  • ^ Klitzing, (x3o3x3x3o3x4o - )
  • ^ Klitzing, (x3x3x3x3o3x4o - )
  • ^ Klitzing, (x3o3o3o3x3x4o - )
  • ^ Klitzing, (x3x3o3o3x3x4o - )
  • ^ Klitzing, (x3o3x3o3x3x4o - )
  • ^ Klitzing, (x3x3x3o3x3x4o - )
  • ^ Klitzing, (x3o3o3x3x3x4o - )
  • ^ Klitzing, (x3x3o3x3x3x4o - )
  • ^ Klitzing, (x3o3x3x3x3x4o - )
  • ^ Klitzing, (x3x3x3x3x3x4o - )

    • References[edit]

    External links[edit]

  • t
  • e
    • Fundamental convex regular and uniform polytopes in dimensions 2–10
    Family An Bn I2(p) / Dn E6 / E7 / E8 / F4 / G2 Hn
    Regular polygon Triangle Square p-gon Hexagon Pentagon
    Uniform polyhedron Tetrahedron Octahedron • Cube Demicube Dodecahedron • Icosahedron
    Uniform polychoron Pentachoron 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

    Retrieved from "https://en.wikipedia.org/w/index.php?title=Pentellated_7-orthoplexes&oldid=1037629745#Pentellated_7-orthoplex"
    Category: 
    ●7-polytopes
      


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