Runcinated 6-cubes

In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube.

There are 12 unique runcinations of the 6-cube with permutations of truncations, and cantellations. 5 are expressed relative to the dual 6-orthoplex.

Runcinated 6-cube

Alternate names

• Small prismated hexeract (spox) (Jonathan Bowers)

Biruncinated 6-cube

Alternate names

• Small biprismated hexeractihexacontatetrapeton (sobpoxog) (Jonathan Bowers)

Runcitruncated 6-cube

Alternate names

• Prismatotruncated hexeract (potax) (Jonathan Bowers)

Biruncitruncated 6-cube

Alternate names

• Biprismatotruncated hexeract (boprag) (Jonathan Bowers)

Runcicantellated 6-cube

Alternate names

• Prismatorhombated hexeract (prox) (Jonathan Bowers)

Runcicantitruncated 6-cube

Alternate names

• Great prismated hexeract (gippox) (Jonathan Bowers)

Biruncicantitruncated 6-cube

Alternate names

• Great biprismated hexeractihexacontatetrapeton (gobpoxog) (Jonathan Bowers)

Related polytopes

These polytopes are from a set of 63 uniform 6-polytopes generated from the B₆ Coxeter plane, including the regular 6-cube and 6-orthoplex.

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.

• o3o3x3o3o4x - spox, o3x3o3o3x4o - sobpoxog, o3o3x3o3x4x - potax, o3x3o3x3x4o - boprag, o3o3x3x3o4x - prox, o3o3x3x3x4x - gippox, o3x3x3x3x4o - gobpoxog

External links

• Polytopes of Various Dimensions
• Multi-dimensional Glossary