6-cubeRuncinated 6-cubeBiruncinated 6-cubeRuncinated 6-orthoplex6-orthoplexRuncitruncated 6-cubeBiruncitruncated 6-cubeRuncicantellated 6-orthoplexRuncicantellated 6-cubeBiruncitruncated 6-orthoplexRuncitruncated 6-orthoplexRuncicantitruncated 6-cubeBiruncicantitruncated 6-cubeRuncicantitruncated 6-orthoplexOrthogonal projections in BC6 Coxeter plane

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

There are 12 unique runcinations of the 6-orthoplex with permutations of truncations, and cantellations. 7 are expressed relative to the dual 6-cube.

Runcinated 6-orthoplex

Alternate names Small prismatohexacontatetrapeton (spog) (Jonathan Bowers)

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Runcicantellated 6-orthoplex

Alternate names Prismatorhombated hexacontatetrapeton (prog) (Jonathan Bowers)

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Biruncitruncated 6-orthoplex

Alternate names Biprismatotruncated hexacontatetrapeton (boprax) (Jonathan Bowers)

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Runcitruncated 6-orthoplex

Alternate names Prismatotruncated hexacontatetrapeton (potag) (Jonathan Bowers)

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Runcicantitruncated 6-orthoplex

Alternate names Great prismated hexacontatetrapeton (gopog) (Jonathan Bowers)

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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.

Notes

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. x3o3o3x3o4o - spog, x3o3x3x3o4o - prog, x3x3o3x3o4o - potag, o3x3x3o3x4o - boprax, x3x3x3x3o4o - gopog

External links

Polytopes of Various Dimensions Multi-dimensional Glossary