- Source: Runcinated 8-simplexes
In eight-dimensional geometry, a runcinated 8-simplex is a convex uniform 8-polytope with 3rd order truncations (runcination) of the regular 8-simplex.
There are eleven unique runcinations of the 8-simplex, including permutations of truncation and cantellation. The triruncinated 8-simplex and triruncicantitruncated 8-simplex have a doubled symmetry, showing [18] order reflectional symmetry in the A8 Coxeter plane.
Runcinated 8-simplex
= Alternate names
=Runcinated enneazetton
Small prismated enneazetton (Acronym: spene) (Jonathan Bowers)
= Coordinates
=The Cartesian coordinates of the vertices of the runcinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 9-orthoplex.
= Images
=Biruncinated 8-simplex
= Alternate names
=Biruncinated enneazetton
Small biprismated enneazetton (Acronym: sabpene) (Jonathan Bowers)
= Coordinates
=The Cartesian coordinates of the vertices of the biruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 9-orthoplex.
= Images
=Triruncinated 8-simplex
= Alternate names
=Triruncinated enneazetton
Small triprismated enneazetton (Acronym: satpeb) (Jonathan Bowers)
= Coordinates
=The Cartesian coordinates of the vertices of the triruncinated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,1,1,1,2,2,2). This construction is based on facets of the triruncinated 9-orthoplex.
= Images
=Runcitruncated 8-simplex
= Images
=Biruncitruncated 8-simplex
= Images
=Triruncitruncated 8-simplex
= Images
=Runcicantellated 8-simplex
= Images
=Biruncicantellated 8-simplex
= Images
=Runcicantitruncated 8-simplex
= Images
=Biruncicantitruncated 8-simplex
= Images
=Triruncicantitruncated 8-simplex
= Images
=Related polytopes
This polytope is one of 135 uniform 8-polytopes with A8 symmetry.
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. "8D uniform polytopes (polyzetta)". x3o3o3x3o3o3o3o - spene, o3x3o3o3x3o3o3o - sabpene, o3o3x3o3o3x3o3o - satpeb
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary