Pentic 6-cubes#Pentic 6-cube

The pentic 6-cube, {{CDD|node_h1|4|node|3|node|3|node|3|node|3|node_1}}, has half of the vertices of a pentellated 6-cube, {{CDD|node_1|4|node|3|node|3|node|3|node|3|node_1}}.

• Stericated 6-demicube
• Stericated demihexeract
• Small cellated hemihexeract (Acronym: sochax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/sochax.htm (x3o3o *b3o3x3o3o - sochax)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±1,±1,±1,±3)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t04|150}}

The penticantic 6-cube, {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node_1}}, has half of the vertices of a penticantellated 6-cube, {{CDD|node_1|4|node|3|node_1|3|node|3|node|3|node_1}}.

• Steritruncated 6-demicube
• Steritruncated demihexeract
• Cellitruncated hemihexeract (Acronym: cathix) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/cathix.htm (x3x3o *b3o3x3o3o - cathix)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±3,±3,±3,±5)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t014|150}}

The pentiruncic 6-cube, {{CDD|node_h1|4|node|3|node|3|node_1|3|node|3|node_1}}, has half of the vertices of a pentiruncinated 6-cube (penticantellated 6-orthoplex), {{CDD|node_1|4|node|3|node|3|node_1|3|node|3|node_1}}.

• Stericantellated 6-demicube
• Stericantellated demihexeract
• Cellirhombated hemihexeract (Acronym: crohax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/crohax.htm (x3o3o *b3x3x3o3o - crohax)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±1,±3,±3,±5)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t024|150}}

The pentiruncicantic 6-cube, {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node|3|node_1}}, has half of the vertices of a pentiruncicantellated 6-cube or (pentiruncicantellated 6-orthoplex), {{CDD|node_1|4|node|3|node_1|3|node_1|3|node|3|node_1}}

• Stericantitruncated demihexeract
• Stericantitruncated 6-demicube
• Great cellated hemihexeract (Acronym: cagrohax) (Jonathan Bowers)Klitzing, (x3x3o *b3x3x3o3o - cagrohax)

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t0124|150}}

The pentisteric 6-cube, {{CDD|node_h1|4|node|3|node|3|node|3|node_1|3|node_1}}, has half of the vertices of a pentistericated 6-cube (pentitruncated 6-orthoplex), {{CDD|node_1|4|node|3|node|3|node|3|node_1|3|node_1}}

• Steriruncinated 6-demicube
• Steriruncinated demihexeract
• Small celliprismated hemihexeract (Acronym: cophix) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/cophix.htm (x3o3o *b3o3x3x3x - cophix)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±1,±1,±3,±5)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t034|150}}

The pentistericantic 6-cube, {{CDD|node_h1|4|node|3|node_1|3|node|3|node_1|3|node_1}}, has half of the vertices of a pentistericantellated 6-cube (pentiruncitruncated 6-orthoplex), {{CDD|node_1|4|node|3|node_1|3|node|3|node_1|3|node_1}}.

• Steriruncitruncated demihexeract
• Steriruncitruncated 6-demicube
• Cellitruncated hemihexeract (Acronym: capthix) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/capthix.htm (x3x3o *b3o3x3x3x - capthix)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t0134|150}}

The pentisteriruncic 6-cube, {{CDD|node_h1|4|node|3|node|3|node_1|3|node_1|3|node_1}}, has half of the vertices of a pentisteriruncinated 6-cube (penticantitruncated 6-orthoplex), {{CDD|node_1|4|node|3|node|3|node_1|3|node_1|3|node_1}}.

• Steriruncicantellated 6-demicube
• Steriruncicantellated demihexeract
• Celliprismatorhombated hemihexeract (Acronym: caprohax) (Jonathan Bowers){{sfn|Klitzing|at=[https://bendwavy.org/klitzing/incmats/caprohax.htm (x3o3o *b3x3x3x3x - caprohax)]}}

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±1,±3,±5,±7)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t0234|150}}

The pentisteriruncicantic 6-cube, {{CDD|node_h1|4|node|3|node_1|3|node_1|3|node_1|3|node_1}}, has half of the vertices of a pentisteriruncicantellated 6-cube (pentisteriruncicantitruncated 6-orthoplex), {{CDD|node_1|4|node|3|node_1|3|node_1|3|node_1|3|node_1}}.

• Steriruncicantitruncated 6-demicube/demihexeract
• Great cellated hemihexeract (Acronym: gochax) (Jonathan Bowers)Klitzing, (x3x3o *b3x3x3x3o - gochax)

The Cartesian coordinates for the vertices, centered at the origin are coordinate permutations:

: (±1,±1,±3,±3,±5,±7)

with an odd number of plus signs.

{{6-demicube Coxeter plane graphs|t01234|150}}

There are 47 uniform polytopes with D₆ symmetry, 31 are shared by the B₆ symmetry, and 16 are unique:

{{Demihexeract_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}} x3o3o *b3o3x3o3o - sochax, x3x3o *b3o3x3o3o - cathix, x3o3o *b3x3x3o3o - crohax, x3x3o *b3x3x3o3o - cagrohax, x3o3o *b3o3x3x3x - cophix, x3x3o *b3o3x3x3x - capthix, x3o3o *b3x3x3x3x - caprohax, x3x3o *b3x3x3x3o - gochax {{sfn whitelist| CITEREFKlitzing}}

• {{MathWorld|title=Hypercube|urlname=Hypercube}}
• [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
• [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]

{{Polytopes}}

Category:6-polytopes