| 释义 |
- Truncated 8-simplex Alternate names Coordinates Images
- Bitruncated 8-simplex Alternate names Coordinates Images
- Tritruncated 8-simplex Alternate names Coordinates Images
- Quadritruncated 8-simplex Alternate names Coordinates Images Related polytopes
- Related polytopes
- Notes
- References
- External links
8-simplex
{{CDD>node_1|3|node|3|node|3|node|3|node|3|node|3|node|3|node}} | Truncated 8-simplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} | Rectified 8-simplex
{{CDD>node|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} | Quadritruncated 8-simplex
{{CDD>node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} | Tritruncated 8-simplex
{{CDD>node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} | Bitruncated 8-simplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}} | | Orthogonal projections in A8 Coxeter plane |
|---|
In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8-simplex. Vertices of the tritruncated 8-simplex are located inside the tetrahedral cells of the 8-simplex. Truncated 8-simplex| Truncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | t{37} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 288 | | Vertices | 72 | | Vertex figure | ( )v{3,3,3,3,3} | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Alternate names- Truncated enneazetton (Acronym: tene) (Jonathan Bowers)[1]
Coordinates The Cartesian coordinates of the vertices of the truncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t01|120px}} Bitruncated 8-simplex| Bitruncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | 2t{37} | | Coxeter-Dynkin diagrams | node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 1008 | | Vertices | 252 | | Vertex figure | { }v{3,3,3,3} | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Alternate names- Bitruncated enneazetton (Acronym: batene) (Jonathan Bowers)[2]
Coordinates The Cartesian coordinates of the vertices of the bitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t12|120px}} Tritruncated 8-simplex| tritruncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | 3t{37} | | Coxeter-Dynkin diagrams | node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} | | 7-faces | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 2016 | | Vertices | 504 | | Vertex figure | {3}v{3,3,3} | | Coxeter group | A8, [37], order 362880 | | Properties | convex |
Alternate names- Tritruncated enneazetton (Acronym: tatene) (Jonathan Bowers)[3]
Coordinates The Cartesian coordinates of the vertices of the tritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 9-orthoplex. Images {{8-simplex Coxeter plane graphs|t23|120px}} Quadritruncated 8-simplex| Quadritruncated 8-simplex | | Type | uniform 8-polytope | | Schläfli symbol | 4t{37} | | Coxeter-Dynkin diagrams | node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}
or {{CDD|branch_11|3ab|nodes|3ab|nodes|3ab|nodes}} | | 6-faces | 18 3t{3,3,3,3,3,3} | | 7-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 2520 | | Vertices | 630 | | Vertex figure |
{3,3}v{3,3} | | Coxeter group | A8, 7">37, order 725760 | | Properties | convex, isotopic |
The quadritruncated 8-simplex an isotopic polytope, constructed from 18 tritruncated 7-simplex facets. Alternate names- Octadecazetton (18-facetted 8-polytope) (Acronym: be) (Jonathan Bowers)[4]
Coordinates The Cartesian coordinates of the vertices of the quadritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,2,2,2,2). This construction is based on facets of the quadritruncated 9-orthoplex. Images {{8-simplex2 Coxeter plane graphs|t34|120px}} Related polytopes{{Isotopic uniform simplex polytopes}} Related polytopes This polytope is one of 135 uniform 8-polytopes with A8 symmetry. {{Enneazetton family}} Notes 1. ^Klitizing, (x3x3o3o3o3o3o3o - tene)
2. ^Klitizing, (o3x3x3o3o3o3o3o - batene)
3. ^Klitizing, (o3o3x3x3o3o3o3o - tatene)
4. ^Klitizing, (o3o3o3x3x3o3o3o - be)
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}}
- (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|polyzetta.htm|8D|uniform polytopes (polyzetta)}} x3x3o3o3o3o3o3o - tene, o3x3x3o3o3o3o3o - batene, o3o3x3x3o3o3o3o - tatene, o3o3o3x3x3o3o3o - be
External links - [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{Polytopes}} 1 : 8-polytopes |