Hexic 7-cubes


7-demicube


Hexic 7-cube


Hexicantic 7-cube


Hexiruncic 7-cube


Hexiruncicantic 7-cube


Hexisteric 7-cube


Hexistericantic 7-cube


Hexisteriruncic 7-cube


Hexisteriruncicantic 7-cube


Hexipentic 7-cube


Hexipenticantic 7-cube


Hexipentiruncic 7-cube


Hexipentiruncicantic 7-cube


Hexipentisteric 7-cube


Hexipentistericantic 7-cube


Hexipentisteriruncic 7-cube


Hexipentisteriruncicantic 7-cube

Orthogonal projections in D7 Coxeter plane

{{-}} In seven-dimensional geometry, a hexic 7-cube is a convex uniform 7-polytope, constructed from the uniform 7-demicube. There are 16 unique forms.

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Hexic 7-cube

Hexic 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 terated demihepteract (acronym: suthesa)

Cartesian coordinates

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

(±1,±1,±1,±1,±1,±1,±3)

with an odd number of plus signs.

Alternate names

  • Teritruncated demihepteract (acronym: tuthesa)

Alternate names

  • Terirhombated demihepteract (acronym: turhesa)

Alternate names

  • Teriprismated demihepteract (acronym: tuphesa)

Alternate names

  • Tericellated demihepteract (acronym: tuchesa)Klitzing, (x3o3o *b3o3o3x3x

- tuchesa)

Alternate names

  • Terigreatorhombated demihepteract (acronym: tugrohesa)

Alternate names

  • Teriprismatotruncated demihepteract (acronym: tupthesa)

Alternate names

  • Tericellitruncated demihepteract (acronym: tucothesa)

Alternate names

  • Teriprismatorhombated demihepteract (acronym: tuprohesa)

Alternate names

  • Tericellirhombated demihepteract (acronym: tucrohesa)

Alternate names

  • Tericelliprismated demihepteract (acronym: tucophesa)

Alternate names

  • Terigreatoprismated demihepteract (acronym: tugphesa)

Alternate names

  • Tericelligreatorhombated demihepteract (acronym: tucagrohesa)

Alternate names

  • Tericelliprismatorhombated demihepteract (acronym: tucprohesa)

Alternate names

  • Tericelliprismatotruncated demihepteract (acronym: tucpathesa)

Alternate names

  • Great terated demihepteract (acronym: guthesa)

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:

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.