| 释义 |
- Truncated 6-orthoplex Alternate names Construction Coordinates Images
- Bitruncated 6-orthoplex Alternate names Images
- Related polytopes
- Notes
- References
- External links
6-orthoplex
{{CDD>node_1|3|node|3|node|3|node|3|node|4|node}} | Truncated 6-orthoplex
{{CDD>node_1|3|node_1|3|node|3|node|3|node|4|node}} | Bitruncated 6-orthoplex
{{CDD>node|3|node_1|3|node_1|3|node|3|node|4|node}} |
Tritruncated 6-cube
{{CDD|node|3|node|3|node_1|3|node_1|3|node|4|node}} | 6-cube
{{CDD>node|3|node|3|node|3|node|3|node|4|node_1}} | Truncated 6-cube
{{CDD>node|3|node|3|node|3|node|3|node_1|4|node_1}} | Bitruncated 6-cube
{{CDD>node|3|node|3|node|3|node_1|3|node_1|4|node}} | | Orthogonal projections in B6 Coxeter plane |
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In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex. There are 5 degrees of truncation for the 6-orthoplex. Vertices of the truncated 6-orthoplex are located as pairs on the edge of the 6-orthoplex. Vertices of the bitruncated 6-orthoplex are located on the triangular faces of the 6-orthoplex. Vertices of the tritruncated 6-orthoplex are located inside the tetrahedral cells of the 6-orthoplex. {{TOC left}}{{-}} Truncated 6-orthoplex | Truncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | t{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node_1|3|node_1|3|node|3|node|3|node|4|node}}
{{CDD|node_1|3|node_1|3|node|3|node|split1|nodes}} | | 5-faces | 76 | | 4-faces | 576 | | Cells | 1200 | | Faces | 1120 | | Edges | 540 | | Vertices | 120 | | Vertex figure |
( )v{3,4} | | Coxeter groups | B6, [3,3,3,3,4]
D6, [33,1,1] | | Properties | convex |
Alternate names- Truncated hexacross
- Truncated hexacontatetrapeton (Acronym: tag) (Jonathan Bowers)[1]
Construction There are two Coxeter groups associated with the truncated hexacross, one with the C6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with the D6 or [33,1,1] Coxeter group. Coordinates Cartesian coordinates for the vertices of a truncated 6-orthoplex, centered at the origin, are all 120 vertices are sign (4) and coordinate (30) permutations of (±2,±1,0,0,0,0) Images{{6-cube Coxeter plane graphs|t45|150}} Bitruncated 6-orthoplex | Bitruncated 6-orthoplex | | Type | uniform 6-polytope | | Schläfli symbol | 2t{3,3,3,3,4} | | Coxeter-Dynkin diagrams | node|3|node_1|3|node_1|3|node|3|node|4|node}}
{{CDD|node|3|node_1|3|node_1|3|node|split1|nodes}} | | 5-faces | | 4-faces | | Cells | | Faces | | Edges | | Vertices | | Vertex figure |
{ }v{3,4} | | Coxeter groups | B6, [3,3,3,3,4]
D6, [33,1,1] | | Properties | convex |
Alternate names- Bitruncated hexacross
- Bitruncated hexacontatetrapeton (Acronym: botag) (Jonathan Bowers)[2]
Images{{6-cube Coxeter plane graphs|t34|150}} Related polytopesThese polytopes are a part of a set of 63 uniform 6-polytopes generated from the B6 Coxeter plane, including the regular 6-cube or 6-orthoplex. {{Hexeract family}} Notes1. ^Klitzing, (x3x3o3o3o4o - tag)
2. ^Klitzing, (o3x3x3o3o4o - botag)
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|polypeta.htm|6D|uniform polytopes (polypeta)}} x3x3o3o3o4o - tag, o3x3x3o3o4o - botag
External links - [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{polytopes}} 1 : 6-polytopes |