Truncated 6-cubes#Tritruncated 6-cube

• Truncated hexeract (Acronym: tox) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/tox.htm (o3o3o3o3x4x - tox)]}}

The truncated 6-cube may be constructed by truncating the vertices of the 6-cube at $1/(\backslash sqrt\{2\}+2)$ of the edge length. A regular 5-simplex replaces each original vertex.

The Cartesian coordinates of the vertices of a truncated 6-cube having edge length 2 are the permutations of:

:$\backslash left(\backslash pm1,\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\}),\backslash \; \backslash pm(1+\backslash sqrt\{2\})\backslash right)$

{{6-cube Coxeter plane graphs|t01|150}}

The truncated 6-cube, is fifth in a sequence of truncated hypercubes:

{{Truncated hypercube polytopes}}

• Bitruncated hexeract (Acronym: botox) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/botox.htm (o3o3o3x3x4o - botox)]}}

The Cartesian coordinates of the vertices of a bitruncated 6-cube having edge length 2 are the permutations of:

:$\backslash left(0,\backslash \; \backslash pm1,\backslash \; \backslash pm2,\backslash \; \backslash pm2,\backslash \; \backslash pm2,\backslash \; \backslash pm2\; \backslash right)$

{{6-cube Coxeter plane graphs|t12|150}}

The bitruncated 6-cube is fourth in a sequence of bitruncated hypercubes:

{{Bitruncated hypercube polytopes}}

• Tritruncated hexeract (Acronym: xog) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/xog.htm (o3o3x3x3o4o - xog)]}}

The Cartesian coordinates of the vertices of a tritruncated 6-cube having edge length 2 are the permutations of:

:$\backslash left(0,\backslash \; 0,\backslash \; \backslash pm1,\backslash \; \backslash pm2,\backslash \; \backslash pm2,\backslash \; \backslash pm2\; \backslash right)$

{{6-cube Coxeter plane graphs|t23|150}}

{{2-isotopic_uniform_hypercube_polytopes}}

The table below contains a set of 63 Uniform 6-polytopes generated from the B₆ Coxeter plane, including the regular 6-cube or 6-orthoplex.

{{Hexeract family}}

{{reflist}}

• 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 Ivic Weiss, Wiley-Interscience Publication, 1995, [https://www.wiley.com/en-us/Kaleidoscopes-p-9780471010036 wiley.com], {{isbn|978-0-471-01003-6}}
• (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.
• {{KlitzingPolytopes|polypeta.htm|6D uniform polytopes (polypeta) with acronyms}} o3o3o3o3x4x - tox, o3o3o3x3x4o - botox, o3o3x3x3o4o - xog {{sfn whitelist| CITEREFKlitzing}}

• {{MathWorld|title=Hypercube|urlname=Hypercube}}
• [http://www.polytope.net/hedrondude/topes.htm Polytopes of Various Dimensions]
• [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:6-polytopes