Runcinerade 6-kuber

Ortogonala projektioner i B ₆ Coxeter-plan
6-kub	Runcinerad 6-kub	Biruncinerad 6-kub	Runcinerad 6-ortoplex	6-ortoplex
Runcitruncated 6-kub	Biruncitruncated 6-kub	Runcikantellerad 6-ortoplex	Runcikantellerad 6-kub	Biruncitruncated 6-ortoplex
Runcitruncated 6-ortoplex	Runcicanti-stympad 6-kub	Biruncicanti-stympad 6-kub	Runcicanti-trunkerad 6-ortoplex

I sexdimensionell geometri är en runcinerad 6-kub en konvex enhetlig 6-polytop med 3:e ordningens trunkationer ( runcination ) av den vanliga 6-kuben .

Det finns 12 unika runcinationer av 6-kuben med permutationer av trunkationer och kantelleringar. Hälften uttrycks i förhållande till det dubbla 6-ortoplexet.

Runcinerad 6-kub

Runcinerad 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _0,3 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	7680
Vertices	1280
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Liten prismatad hexeract (spox) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Biruncinerad 6-kub

Biruncinerad 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _1,4 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	11520
Vertices	1920
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Liten biprismatad hexeractihexacontatetrapeton (sobpoxog) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Runcitruncated 6-kub

Runcitruncated 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _0,1,3 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	17280
Vertices	3840
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Prismatotruncated hexeract (potax) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Biruncitruncated 6-kub

Biruncitruncated 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _1,2,4 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	23040
Vertices	5760
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Biprismatotruncated hexeract (boprag) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Runcikantellerad 6-kub

Runcikantellerad 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _0,2,3 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	13440
Vertices	3840
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Prismatorhombated hexeract (prox) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Runcicantitruncerad 6-kub

Runcicantitruncerad 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _0,1,2,3 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	23040
Vertices	7680
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Stor prismatad hexeract (gippox) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Biruncitruncated 6-kub

Biruncitruncated 6-kub
Typ	Uniform 6-polytop
Schläfli symbol	t _1,2,3,4 {4,3,3,3,3}
Coxeter-Dynkin diagram
4-faces
Cells
Faces
Kanter	23040
Vertices	5760
Vertex figur
Coxeter grupp	B ₆ [4,3,3,3,3]
Egenskaper	konvex

Alternativa namn

Biprismatotruncated hexeract (boprag) (Jonathan Bowers)

Bilder

ortografiska projektioner
Coxeter plan	B ₆	B ₅	B ₄
Graf
Dihedral symmetri	[12]	[10]	[8]
Coxeter plan	B ₃	B ₂
Graf
Dihedral symmetri	[6]	[4]
Coxeter plan	En ₅	A ₃
Graf
Dihedral symmetri	[6]	[4]

Besläktade polytoper

Dessa polytoper är från en uppsättning av 63 enhetliga 6-polytoper genererade från B ₆ Coxeter-planet , inklusive den vanliga 6-kuben eller 6-ortoplexen .

B6 polytoper
β ₆	t ₁ β ₆	t ₂ β ₆	t ₂ y ₆	t ₁ y ₆	γ ₆	t _0,1 β ₆	t _0,2 β ₆
t _1,2 β ₆	t _0,3 β ₆	t _1,3 β ₆	t _2,3 y ₆	t _0,4 β ₆	t _1,4 y ₆	t _1,3 y ₆	t _1,2 y ₆
t _0,5 y ₆	t _0,4 y ₆	t _0,3 y ₆	t _0,2 y ₆	t _0,1 y ₆	t _0,1,2 P6 _{_}	t _0,1,3 P6 _{_}	t _0,2,3 p6 _{_}
t _1,2,3 β ₆	t _0,1,4 P6 _{_}	t _0,2,4 P6 _{_}	t _1,2,4 P6 _{_}	t _0,3,4 P6 _{_}	t _1,2,4 y ₆	t _1,2,3 y ₆	t _0,1,5 p6 _{_}
t _0,2,5 β ₆	t _0,3,4 y ₆	t _0,2,5 y ₆	t _0,2,4 y ₆	t _0,2,3 y ₆	t _0,1,5 y ₆	t _0,1,4 y ₆	t _0,1,3 y ₆
t _0,1,2 y ₆	t _0,1,2,3 P6 _{_}	t _0,1,2,4 P6 _{_}	t _0,1,3,4 P6 _{_}	t _0,2,3,4 P6 _{_}	t _1,2,3,4 y ₆	t _0,1,2,5 p6 _{_}	t _0,1,3,5 β ₆
t _0,2,3,5 y ₆	t _0,2,3,4 y ₆	t _0,1,4,5 y ₆	t _0,1,3,5 y ₆	t _0,1,3,4 y ₆	t _0,1,2,5 y ₆	t _0,1,2,4 y ₆	t _0,1,2,3 y ₆
t _0,1,2,3,4 β ₆	t _0,1,2,3,5 β6 _{_}	t _0,1,2,4,5 β6 _{_}	t _0,1,2,4,5 y ₆	t _0,1,2,3,5 y ₆	t _0,1,2,3,4 y ₆	t _0,1,2,3,4,5 y ₆

Anteckningar

HSM Coxeter :
- HSM Coxeter, Regular Polytopes , 3:e upplagan, Dover New York, 1973
- Kaleidoscopes: Selected Writings of HSM Coxeter , redigerad av F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
  - (Papper 22) HSM Coxeter, Regular and Semi Regular Polytopes I , [Math. Zeit. 46 (1940) 380-407, MR 2,10]
  - (Papper 23) HSM Coxeter, Regular and Semi-Regular Polytopes II , [Math. Zeit. 188 (1985) 559-591]
  - (Papper 24) HSM Coxeter, Regular and Semi-Regular Polytopes III , [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes , Manuscript (1991)
- NW Johnson: Theory of Uniform Polytopes and Honeycombs , Ph.D.
Klitzing, Richard. "6D enhetliga polytoper (polypeta)" . o3o3x3o3o4x - spox, o3x3o3o3x4o - sobpoxog, o3o3x3o3x4x - potax, o3x3o3x3x4o - boprag, o3o3x3x3o4x - prox, o3o3x3x3x4x - gippox, o3xo, o3xo

externa länkar

Grundläggande konvexa regelbundna och enhetliga polytoper i dimensionerna 2–10
Familj	A _n	B _n	I ₂ (p) / D _n	E ₆ / E ₇ / E ₈ / F ₄ / G ₂	H _n
Vanlig polygon	Triangel	Fyrkant	p-gon	Sexhörning	Pentagon
Uniform polyeder	Tetraeder	Oktaeder • Kub	Demicube		Dodekaeder • Ikosaeder
Uniform polychoron	Pentachoron	16-celler • Tesseract	Demitesseract	24-celler	120-celler • 600-celler
Uniform 5-polytop	5-simplex	5-ortoplex • 5-kub	5-demikub
Uniform 6-polytop	6-simplex	6-ortoplex • 6-kub	6-demikub	1 ₂₂ • 2 ₂₁
Uniform 7-polytop	7-simplex	7-ortoplex • 7-kub	7-demikub	1 ₃₂ • 2 ₃₁ • 3 ₂₁
Uniform 8-polytop	8-simplex	8-ortoplex • 8-kub	8-demikub	1 ₄₂ • 2 ₄₁ • 4 ₂₁
Uniform 9-polytop	9-simplex	9-ortoplex • 9-kub	9-demikub
Uniform 10-polytop	10-simplex	10-ortoplex • 10-kub	10-demikub
Uniform n - polytop	n - simplex	n - ortoplex • n - kub	n - demikub	1 _k2 • 2 _k1 • k ₂₁	n - femkantig polytop
Ämnen: Polytopfamiljer • Vanlig polytop • Lista över vanliga polytoper och sammansättningar