Pentic 7-cubes

7-demicube t01234 D7


7-demicube
(half 7-cube, h{4,35})


Pentic 7-cube
h5{4,35}


Penticantic 7-cube
h2,5{4,35}


Pentiruncic 7-cube
h3,5{4,35}


Pentiruncicantic 7-cube
h2,3,5{4,35}


Pentisteric 7-cube
h4,5{4,35}


Pentistericantic 7-cube
h2,4,5{4,35}


Pentisteriruncic 7-cube
h3,4,5{4,35}


Penticsteriruncicantic 7-cube
h2,3,4,5{4,35}

Orthogonal projections in D7 Coxeter plane

In seven-dimensional geometry, a pentic 7-cube is a convex uniform 7-polytope, related to the uniform 7-demicube. There are 8 unique forms.

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Pentic 7-cube

Pentic 7-cube

Type

Schläfli symbol

Coxeter-Dynkin diagram

6-faces

5-faces

4-faces

Cells

Faces

Edges

Vertices

Vertex figure

Coxeter groups

Properties

Alternate names

  • Small cellated demihepteract (acronym: sochesa)

Cartesian coordinates

The Cartesian coordinates for the vertices of a pentic 7-cube centered at the origin are coordinate permutations:

(±1,±1,±1,±1,±1,±3,±3)

with an odd number of plus signs.

Alternate names

  • Cellitruncated demihepteract (acronym: cothesa)

Alternate names

  • Cellirhombated demihepteract (acronym: crohesa)

Alternate names

  • Celligreatorhombated demihepteract (acronym: cagrohesa)

Alternate names

  • Celliprismated demihepteract (acronym: caphesa)

Alternate names

  • Celliprismatotruncated demihepteract (acronym: capthesa)

Alternate names

  • Celliprismatorhombated demihepteract (acronym: coprahesa)

Alternate names

  • Great cellated demihepteract (acronym: gochesa)

These polytopes are based on the 7-demicube, a member of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.

There are 95 uniform polytopes with D7 symmetry, 63 are shared by the BC7 symmetry, and 32 are unique:

7-demicube t0124 D7
7-demicube t0134 D7
7-demicube t014 D7
7-demicube t0234 D7
7-demicube t024 D7
7-demicube t034 D7
7-demicube t04 D7
7-demicube t0 D7

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.

See Also

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