| 释义 |
- Truncated 8-cube Alternate names Coordinates Images Related polytopes
- Bitruncated 8-cube Alternate names Coordinates Images Related polytopes
- Tritruncated 8-cube Alternate names Coordinates Images
- Quadritruncated 8-cube Alternate names Coordinates Images Related polytopes
- Notes
- References
- External links
8-cube
{{CDD>node_1|4|node|3|node|3|node|3|node|3|node|3|node|3|node}} | Truncated 8-cube
{{CDD>node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} | Bitruncated 8-cube
{{CDD>node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}} | Quadritruncated 8-cube
{{CDD>node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|4|node}} | Tritruncated 8-cube
{{CDD>node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}} | Tritruncated 8-orthoplex
{{CDD>node|4|node|3|node|3|node|3|node_1|3|node_1|3|node|3|node}} | Bitruncated 8-orthoplex
{{CDD>node|4|node|3|node|3|node|3|node|3|node_1|3|node_1|3|node}} | Truncated 8-orthoplex
{{CDD>node|4|node|3|node|3|node|3|node|3|node|3|node_1|3|node_1}} | 8-orthoplex
{{CDD>node|4|node|3|node|3|node|3|node|3|node|3|node|3|node_1}} | | Orthogonal projections in B8 Coxeter plane |
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In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube. There are unique 7 degrees of truncation for the 8-cube. Vertices of the truncation 8-cube are located as pairs on the edge of the 8-cube. Vertices of the bitruncated 8-cube are located on the square faces of the 8-cube. Vertices of the tritruncated 7-cube are located inside the cubic cells of the 8-cube. The final truncations are best expressed relative to the 8-orthoplex. {{TOC left}}{{-}} Truncated 8-cube | Truncated 8-cube | | Type | uniform 8-polytope | | Schläfli symbol | t{4,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node_1|4|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | ( )v{3,3,3,3,3} | | Coxeter groups | B8, [3,3,3,3,3,3,4] | | Properties | convex |
Alternate names - Truncated octeract (acronym tocto) (Jonathan Bowers)[1]
Coordinates Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of (±2,±2,±2,±2,±2,±2,±1,0) Images {{8-cube Coxeter plane graphs|t01|200}} Related polytopes The truncated 8-cube, is seventh in a sequence of truncated hypercubes: {{Truncated hypercube polytopes}} Bitruncated 8-cube | Bitruncated 8-cube | | Type | uniform 8-polytope | | Schläfli symbol | 2t{4,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node|4|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | { }v{3,3,3,3} | | Coxeter groups | B8, [3,3,3,3,3,3,4] | | Properties | convex |
Alternate names - Bitruncated octeract (acronym bato) (Jonathan Bowers)[2]
Coordinates Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of (±2,±2,±2,±2,±2,±1,0,0) Images {{8-cube Coxeter plane graphs|t12|200}} Related polytopes The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes: {{Bitruncated hypercube polytopes}} Tritruncated 8-cube | Tritruncated 8-cube | | Type | uniform 8-polytope | | Schläfli symbol | 3t{4,3,3,3,3,3,3} | | Coxeter-Dynkin diagrams | node|4|node|3|node_1|3|node_1|3|node|3|node|3|node|3|node}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | {4}v{3,3,3} | | Coxeter groups | B8, [3,3,3,3,3,3,4] | | Properties | convex |
Alternate names - Tritruncated octeract (acronym tato) (Jonathan Bowers)[3]
Coordinates Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of (±2,±2,±2,±2,±1,0,0,0) Images {{8-cube Coxeter plane graphs|t23|200}} Quadritruncated 8-cube | Quadritruncated 8-cube | | Type | uniform 8-polytope | | Schläfli symbol | 4t{3,3,3,3,3,3,4} | | Coxeter-Dynkin diagrams | node|4|node|3|node|3|node_1|3|node_1|3|node|3|node|3|node}}
{{CDD|node|3|node|3|node|3|node_1|3|node_1|3|node|split1|nodes}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure | {3,4}v{3,3} | | Coxeter groups | B8, [3,3,3,3,3,3,4]
D8, [35,1,1] | | Properties | convex |
Alternate names - Quadritruncated octeract (acronym oke) (Jonathan Bowers)[4]
Coordinates Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of (±2,±2,±2,±2,±1,0,0,0) Images {{8-cube Coxeter plane graphs|t34|200}} Related polytopes{{2-isotopic_uniform_hypercube_polytopes}} Notes1. ^Klitizing, (o3o3o3o3o3o3x4x – tocto)
2. ^Klitizing, (o3o3o3o3o3x3x4o – bato)
3. ^Klitizing, (o3o3o3o3x3x3o4o – tato)
4. ^Klitizing, (o3o3o3x3x3o3o4o – oke)
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)}} o3o3o3o3o3o3x4x – tocto, o3o3o3o3o3x3x4o – bato, o3o3o3o3x3x3o4o – tato, o3o3o3x3x3o3o4o – oke
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 |