| 释义 |
- Truncated 7-orthoplex Alternate names Coordinates Images Construction
- Bitruncated 7-orthoplex Alternate names Coordinates Images
- Tritruncated 7-orthoplex Alternate names Coordinates Images
- Notes
- References
- External links
7-orthoplex
{{CDD>node_1|3|node|3|node|3|node|3|node|3|node|4|node}} | Truncated 7-orthoplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node|3|node|4|node}} | Bitruncated 7-orthoplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node|3|node|4|node}} | Tritruncated 7-orthoplex
{{CDD>node|3|node|3|node_1|3|node_1|3|node|3|node|4|node}} | 7-cube
{{CDD>node|3|node|3|node|3|node|3|node|3|node|4|node_1}} | Truncated 7-cube
{{CDD>node|3|node|3|node|3|node|3|node|3|node_1|4|node_1}} | Bitruncated 7-cube
{{CDD>node|3|node|3|node|3|node|3|node_1|3|node_1|4|node}} | Tritruncated 7-cube
{{CDD>node|3|node|3|node|3|node_1|3|node_1|3|node|4|node}} | | Orthogonal projections in B7 Coxeter plane |
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In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex. There are 6 truncations of the 7-orthoplex. Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex. Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube. {{TOC left}}{{-}} Truncated 7-orthoplex | Truncated 7-orthoplex | | Type | uniform 7-polytope | | Schläfli symbol | t{35,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node|3|node|3|node|split1|nodes}} | | 6-faces | | 5-faces | | 4-faces | | Cells | 3920 | | Faces | 2520 | | Edges | 924 | | Vertices | 168 | | Vertex figure | ( )v{3,3,4} | | Coxeter groups | B7, [35,4]
D7, [34,1,1] | | Properties | convex |
Alternate names- Truncated heptacross
- Truncated hecatonicosoctaexon (Jonathan Bowers)[1]
Coordinates Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign (4) and coordinate (42) permutations of (±2,±1,0,0,0,0,0) Images {{7-cube Coxeter plane graphs|t56|150}} Construction There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or [4,35] Coxeter group, and a lower symmetry with the D7 or [34,1,1] Coxeter group. Bitruncated 7-orthoplex | Bitruncated 7-orthoplex | | Type | uniform 7-polytope | | Schläfli symbol | 2t{35,4} | | Coxeter-Dynkin diagrams | node|3|node_1|3|node_1|3|node|3|node|3|node|4|node}}
{{CDD|node|3|node_1|3|node_1|3|node|3|node|split1|nodes}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 4200 | | Vertices | 840 | | Vertex figure | { }v{3,3,4} | | Coxeter groups | B7, [35,4]
D7, [34,1,1] | | Properties | convex |
Alternate names- Bitruncated heptacross
- Bitruncated hecatonicosoctaexon (Jonathan Bowers)[2]
Coordinates Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of (±2,±2,±1,0,0,0,0) Images{{7-cube Coxeter plane graphs|t45|150}} Tritruncated 7-orthoplex The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb. | Tritruncated 7-orthoplex | | Type | uniform 7-polytope | | Schläfli symbol | 3t{35,4} | | Coxeter-Dynkin diagrams | node|3|node|3|node_1|3|node_1|3|node|3|node|4|node}}
{{CDD|node|3|node|3|node_1|3|node_1|3|node|split1|nodes}} | | 6-faces | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | 10080 | | Vertices | 2240 | | Vertex figure | {3}v{3,4} | | Coxeter groups | B7, [35,4]
D7, [34,1,1] | | Properties | convex |
Alternate names- Tritruncated heptacross
- Tritruncated hecatonicosoctaexon (Jonathan Bowers)[3]
Coordinates Cartesian coordinates for the vertices of a tritruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of (±2,±2,±2,±1,0,0,0) Images{{7-cube Coxeter plane graphs|t34|150}} Notes1. ^Klitzing, (x3x3o3o3o3o4o - tez)
2. ^Klitzing, (o3x3x3o3o3o4o - botaz)
3. ^Klitzing, (o3o3x3x3o3o4o - totaz)
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|polyexa.htm|7D|uniform polytopes (polyexa)}} x3x3o3o3o3o4o - tez, o3x3x3o3o3o4o - botaz, o3o3x3x3o3o4o - totaz
External links - [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{polytopes}} 1 : 7-polytopes |