| 释义 |
- Truncated 5-orthoplex Alternate names Coordinates Images
- Bitruncated 5-orthoplex Alternate names Coordinates Images
- Related polytopes
- Notes
- References
- External links
5-orthoplex
{{CDD>node_1|3|node|3|node|3|node|4|node}} | Truncated 5-orthoplex
{{CDD>node_1|3|node_1|3|node|3|node|4|node}} | Bitruncated 5-orthoplex
{{CDD>node|3|node_1|3|node_1|3|node|4|node}} | 5-cube
{{CDD>node|3|node|3|node|3|node|4|node_1}} | Truncated 5-cube
{{CDD>node|3|node|3|node|3|node_1|4|node_1}} | Bitruncated 5-cube
{{CDD>node|3|node|3|node_1|3|node_1|4|node}} | | Orthogonal projections in B5 Coxeter plane |
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In six-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex. There are 4 unique truncations of the 5-orthoplex. Vertices of the truncation 5-orthoplex are located as pairs on the edge of the 5-orthoplex. Vertices of the bitruncated 5-orthoplex are located on the triangular faces of the 5-orthoplex. The third and fourth truncations are more easily constructed as second and first truncations of the 5-cube. {{TOC left}}{{-}} Truncated 5-orthoplex | Truncated 5-orthoplex | | Type | uniform 5-polytope | | Schläfli symbol | t{3,3,3,4}
t{3,31,1} | | Coxeter-Dynkin diagrams | {{CDD | 4|node | node|3|node_1 | node_1}}
{{CDD|nodes|split2|node|3|node_1 | node_1} | | 4-faces | 42 | | Cells | 240 | | Faces | 400 | | Edges | 280 | | Vertices | 80 | | Vertex figure |
( )v{3,4} | | Coxeter groups | B5, [3,3,3,4]
D5, [32,1,1] | | Properties | convex |
Alternate names- Truncated pentacross
- Truncated triacontiditeron (Acronym: tot) (Jonathan Bowers)[1]
Coordinates Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of (±2,±1,0,0,0) Images The trunacted 5-orthoplex is constructed by a truncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge. {{5-cube Coxeter plane graphs|t34|150}} Bitruncated 5-orthoplex | Bitruncated 5-orthoplex | | Type | uniform 5-polytope | | Schläfli symbol | 2t{3,3,3,4}
2t{3,31,1} | | Coxeter-Dynkin diagrams | {{CDD | 4|node | node_1|3|node_1 | node}}
{{CDD|nodes|split2|node_1|3|node_1 | node} | | 4-faces | 42 | | Cells | 280 | | Faces | 720 | | Edges | 720 | | Vertices | 240 | | Vertex figure |
{ }v{4} | | Coxeter groups | B5, [3,3,3,4]
D5, [32,1,1] | | Properties | convex |
The bitruncated 5-orthoplex can tessellate space in the tritruncated 5-cubic honeycomb. Alternate names- Bitruncated pentacross
- Bitruncated triacontiditeron (acronym: gart) (Jonathan Bowers)[2]
Coordinates Cartesian coordinates for the vertices of a truncated 5-orthoplex, centered at the origin, are all 80 vertices are sign and coordinate permutations of (±2,±2,±1,0,0) Images The bitrunacted 5-orthoplex is constructed by a bitruncation operation applied to the 5-orthoplex. All edges are shortened, and two new vertices are added on each original edge. {{5-cube Coxeter plane graphs|t23|150}} Related polytopesThis polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex. {{Penteract family}} Notes1. ^Klitzing, (x3x3o3o4o - tot)
2. ^Klitzing, (x3x3x3o4o - gart)
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|polytera.htm|5D|uniform polytopes (polytera)}} x3x3o3o4o - tot, x3x3x3o4o - gart
External links - {{MathWorld|title=Hypercube|urlname=Hypercube}}
- [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- Multi-dimensional Glossary
{{Polytopes}} 1 : 5-polytopes |