Hexic 7-cubes

{{-}} 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

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)

Related polytopes

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.

External links

• Polytopes of Various Dimensions
• Multi-dimensional Glossary