释义 |
- Truncated 8-orthoplex Alternate names Construction Coordinates Images
- Bitruncated 8-orthoplex Alternate names Coordinates Images
- Tritruncated 8-orthoplex Alternate names Coordinates Images
- Notes
- References
- External links
8-orthoplex {{CDD>node_1|3|node|3|node|3|node|3|node|3|node|3|node|4|node}} | Truncated 8-orthoplex {{CDD>node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|4|node}} | Bitruncated 8-orthoplex {{CDD>node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|4|node}} | Tritruncated 8-orthoplex {{CDD>node|3|node|3|node|3|node_1|3|node_1|3|node|3|node|4|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|3|node|3|node|3|node|3|node_1|3|node_1|3|node|4|node}} | Bitruncated 8-cube {{CDD>node|3|node|3|node|3|node|3|node|3|node_1|3|node_1|4|node}} | Truncated 8-cube {{CDD>node|3|node|3|node|3|node|3|node|3|node|3|node_1|4|node_1}} | 8-cube {{CDD>node|3|node|3|node|3|node|3|node|3|node|3|node|4|node_1}} | Orthogonal projections in B8 Coxeter plane |
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In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex. There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube. {{TOC left}}{{-}} Truncated 8-orthoplex Truncated 8-orthoplex | Type | uniform 8-polytope | Schläfli symbol | t0,1{3,3,3,3,3,3,4} | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node|3|node|3|node|3|node}} {{CDD|node_1|3|node_1|3|node|3|node|3|node|3|node|split1|nodes}} | 6-faces | 5-faces | 4-faces | Cells | Faces | Edges | 1456 | Vertices | 224 | Vertex figure | ( )v{3,3,3,4} | Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [35,1,1] | Properties | convex |
Alternate names - Truncated octacross (acronym tek) (Jonthan Bowers)[1]
Construction There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [35,1,1] Coxeter group. Coordinates Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of (±2,±1,0,0,0,0,0,0) Images {{8-cube Coxeter plane graphs|t67|200}} Bitruncated 8-orthoplex Bitruncated 8-orthoplex | Type | uniform 8-polytope | Schläfli symbol | t1,2{3,3,3,3,3,3,4} | Coxeter-Dynkin diagrams | node|3|node_1|3|node_1|3|node|3|node|3|node|3|node|3|node}} {{CDD|node|3|node_1|3|node_1|3|node|3|node|3|node|split1|nodes}} | 6-faces | 5-faces | 4-faces | Cells | Faces | Edges | Vertices | Vertex figure | { }v{3,3,3,4} | Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [35,1,1] | Properties | convex |
Alternate names - Bitruncated octacross (acronym batek) (Jonthan Bowers)[2]
Coordinates Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of (±2,±2,±1,0,0,0,0,0) Images {{8-cube Coxeter plane graphs|t56|200}} Tritruncated 8-orthoplex Tritruncated 8-orthoplex | Type | uniform 8-polytope | Schläfli symbol | t2,3{3,3,3,3,3,3,4} | Coxeter-Dynkin diagrams | node|3|node|3|node_1|3|node_1|3|node|3|node|3|node|4|node}} {{CDD|node|3|node|3|node_1|3|node_1|3|node|3|node|split1|nodes}} | 6-faces | 5-faces | 4-faces | Cells | Faces | Edges | Vertices | Vertex figure | {3}v{3,3,4} | Coxeter groups | B8, [3,3,3,3,3,3,4] D8, [35,1,1] | Properties | convex |
Alternate names - Tritruncated octacross (acronym tatek) (Jonthan Bowers)[3]
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,±1,0,0,0,0) Images {{8-cube Coxeter plane graphs|t45|200}} Notes1. ^Klitizing, (x3x3o3o3o3o3o4o - tek) 2. ^Klitizing, (o3x3x3o3o3o3o4o - batek) 3. ^Klitizing, (o3o3x3x3o3o3o4o - tatek)
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. (1966)
- {{KlitzingPolytopes|polyzetta.htm|8D|uniform polytopes (polyzetta)}} x3x3o3o3o3o3o4o - tek, o3x3x3o3o3o3o4o - batek, o3o3x3x3o3o3o4o - tatek
External links - Polytopes of Various Dimensions
- Multi-dimensional Glossary
{{Polytopes}} 1 : 8-polytopes |