Hispanopedia WikiIn eight-dimensional geometry, a stericated 8-simplex is a convex uniform 8-polytope with 4th order truncations (sterication) of the regular 8-simplex. There are 16 unique sterications for the 8-simplex including permutations of truncation, cantellation, and runcination.
Stericated 8-simplex
Acronym: secane (Jonathan Bowers)[1]
Coordinates
The Cartesian coordinates of the vertices of the stericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,1,2). This construction is based on facets of the stericated 9-orthoplex.
Images
Bistericated 8-simplex
Acronym: sobcane (Jonathan Bowers)[2]
Coordinates
The Cartesian coordinates of the vertices of the bistericated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,1,2,2). This construction is based on facets of the bistericated 9-orthoplex.
Images
Steritruncated 8-simplex
Acronym: catene (Jonathan Bowers)[3]
Images
Bisteritruncated 8-simplex
Acronym: bictane (Jonathan Bowers)[4]
Images
Stericantellated 8-simplex
Acronym: crane (Jonathan Bowers)[5]
Images
Bistericantellated 8-simplex
Acronym: bocrane (Jonathan Bowers)[6]
Images
Stericantitruncated 8-simplex
Acronym: cograne (Jonathan Bowers)[7]
Images
Bistericantitruncated 8-simplex
Acronym: bocagrane (Jonathan Bowers)[8]
Images
Steriruncinated 8-simplex
Acronym: capene (Jonathan Bowers)[9]
Images
Bisteriruncinated 8-simplex
Acronym: bacpane (Jonathan Bowers)[10]
Images
Steriruncitruncated 8-simplex
Acronym: coptane (Jonathan Bowers)[11]
Images
Bisteriruncitruncated 8-simplex
Acronym: bicpotane (Jonathan Bowers)[12]
Images
Steriruncicantellated 8-simplex
Acronym: coprene (Jonathan Bowers)[13]
Images
Bisteriruncicantellated 8-simplex
Acronym: bicprene (Jonathan Bowers)[14]
Images
Steriruncicantitruncated 8-simplex
Acronym: gacene (Jonathan Bowers)[15]
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Bisteriruncicantitruncated 8-simplex
Acronym: gobcane (Jonathan Bowers)[16]
Images
Related polytopes
The 16 presented polytopes are in the family of 135 uniform 8-polytopes with A8 symmetry.
Notes
- ↑Klitzing, (x3o3o3o3x3o3o3o - secane)
- ↑Klitzing, (o3x3o3o3o3x3o3o - sobcane)
- ↑Klitzing, (x3x3o3o3x3o3o3o - catene)
- ↑Klitzing, (o3x3x3o3o3x3o3o - bictane)
- ↑Klitzing, (x3o3x3o3x3o3o3o - crane)
- ↑Klitzing, (o3x3o3x3o3x3o3o - bocrane)
- ↑Klitzing, (x3x3x3o3x3o3o3o - cograne)
- ↑Klitzing, (o3x3x3x3ox3o3o3 - bocagrane)
- ↑Klitzing, (x3o3o3x3x3o3o3o - capene)
- ↑Klitzing, (o3x3o3o3x3x3o3o - bacpane)
- ↑Klitzing, (x3x3o3x3x3o3o3o - coptane)
- ↑Klitzing, (o3x3x3o3x3x3o3o - bicpotane)
- ↑Klitzing, (x3o3x3x3x3o3o3o - coprene)
- ↑Klitzing, (o3x3o3x3x3x3o3o - bicprene)
- ↑ Klitzing, (x3x3x3x3x3o3o3o - gacene)
- ↑ Klitzing, (o3x3x3x3x3x3o3o - gobcane)
Referencias
- HSM Coxeter :
- HSM Coxeter, Politopos regulares , 3.ª edición, Dover, Nueva York, 1973
- Caleidoscopios: Escritos selectos de HSM Coxeter , editado por F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivić Weiss, Wiley-Interscience Publication, 1995, wiley.com , ISBN 978-0-471-01003-6
- (Artículo 22) HSM Coxeter, Politopos regulares y semi-regulares I , [Math. Zeit. 46 (1940) 380–407, MR 2,10]
- (Artículo 23) HSM Coxeter, Politopos regulares y semi-regulares II , [Math. Zeit. 188 (1985) 559–591]
- (Artículo 24) HSM Coxeter, Politopos regulares y semi-regulares III , [Math. Zeit. 200 (1988) 3–45]
- Norman Johnson, Politopos Uniformes , Manuscrito (1991)
- NW Johnson: La teoría de los politopos uniformes y los panales de abeja , tesis doctoral.
- Klitzing, Richard. "Polítopos uniformes 8D (polyzetta)" .x3o3o3o3x3o3o3o - secane, o3x3o3o3o3x3o3o - sobcane, x3x3o3o3x3o3o3o - catene, o3x3x3o3o3x3o3o - bictane, x3o3x3o3x3o3o3o - grúa, o3x3o3x3o3x3o3o - bocrane, x3x3x3o3x3o3o3o - cograne, o3x3x3x3ox3o3o3 - bocagrane, x3o3o3x3x3o3o3o - capene, o3x3o3o3x3x3o3o - bacpane, x3x3o3x3x3o3o3o - coptano, o3x3x3o3x3x3o3o - bipotano, x3o3x3x3x3o3o3o - copreno, o3x3o3x3x3x3o3o - bicpreno, x3x3x3x3x3o3o3o - gaceno, o3x3x3x3x3x3o3o - gobcane
Enlaces externos
- Politopos de diversas dimensiones
- Glosario multidimensional
- 8-polytopes