- Source: Pentic 6-cubes
In six-dimensional geometry, a pentic 6-cube is a convex uniform 6-polytope.
There are 8 pentic forms of the 6-cube.
Pentic 6-cube
The pentic 6-cube, , has half of the vertices of a pentellated 6-cube, .
= Alternate names
=Stericated 6-demicube/demihexeract
Small cellated hemihexeract (Acronym: sochax) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Penticantic 6-cube
The penticantic 6-cube, , has half of the vertices of a penticantellated 6-cube, .
= Alternate names
=Steritruncated 6-demicube/demihexeract
cellitruncated hemihexeract (Acronym: cathix) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentiruncic 6-cube
The pentiruncic 6-cube, , has half of the vertices of a pentiruncinated 6-cube (penticantellated 6-orthoplex), .
= Alternate names
=Stericantellated 6-demicube/demihexeract
cellirhombated hemihexeract (Acronym: crohax) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentiruncicantic 6-cube
The pentiruncicantic 6-cube, , has half of the vertices of a pentiruncicantellated 6-cube or (pentiruncicantellated 6-orthoplex),
= Alternate names
=Stericantitruncated demihexeract, stericantitruncated 7-demicube
Great cellated hemihexeract (Acronym: cagrohax) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentisteric 6-cube
The pentisteric 6-cube, , has half of the vertices of a pentistericated 6-cube (pentitruncated 6-orthoplex),
= Alternate names
=Steriruncinated 6-demicube/demihexeract
Small cellipriamated hemihexeract (Acronym: cophix) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentistericantic 6-cube
The pentistericantic 6-cube, , has half of the vertices of a pentistericantellated 6-cube (pentiruncitruncated 6-orthoplex), .
= Alternate names
=Steriruncitruncated demihexeract/7-demicube
cellitruncated hemihexeract (Acronym: capthix) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentisteriruncic 6-cube
The pentisteriruncic 6-cube, , has half of the vertices of a pentisteriruncinated 6-cube (penticantitruncated 6-orthoplex), .
= Alternate names
=Steriruncicantellated 6-demicube/demihexeract
Celliprismatorhombated hemihexeract (Acronym: caprohax) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Pentisteriruncicantic 6-cube
The pentisteriruncicantic 6-cube, , has half of the vertices of a pentisteriruncicantellated 6-cube (pentisteriruncicantitruncated 6-orthoplex), .
= Alternate names
=Steriruncicantitruncated 6-demicube/demihexeract
Great cellated hemihexeract (Acronym: gochax) (Jonathan Bowers)
= Cartesian coordinates
=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.
= Images
=Related polytopes
There are 47 uniform polytopes with D6 symmetry, 31 are shared by the B6 symmetry, and 16 are unique:
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 Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
(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.
Klitzing, Richard. "6D uniform polytopes (polypeta)". x3o3o *b3o3x3o3o - sochax, x3x3o *b3o3x3o3o - cathix, x3o3o *b3x3x3o3o - crohax, x3x3o *b3x3x3o3o - cagrohax, x3o3o *b3o3x3x3x - cophix, x3x3o *b3o3x3x3x - capthix, x3o3o *b3x3x3x3x - caprohax, x3x3o *b3x3x3x3o - gochax
External links
Weisstein, Eric W. "Hypercube". MathWorld.
Polytopes of Various Dimensions
Multi-dimensional Glossary
Kata Kunci Pencarian:
- Pentic 6-cubes
- Pentic 7-cubes
- Uniform 8-polytope
- Uniform 6-polytope
- D6 polytope
- Quarter 8-cubic honeycomb
- Uniform 7-polytope
- D7 polytope
- D8 polytope
