Cantic 8-cube#Truncated 8-demicube
{{Short description|A uniform 8-polytope}}
| class="wikitable" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Cantic 8-cube | |
| bgcolor=#ffffff align=center colspan=2|280px D8 Coxeter plane projection | |
| bgcolor=#e7dcc3|Type | uniform 8-polytope |
| bgcolor=#e7dcc3|Schläfli symbol | t0,1{3,35,1} h2{4,3,3,3,3,3,3} |
| bgcolor=#e7dcc3|Coxeter-Dynkin diagram | {{CDD|nodes_10ru|split2|node_1|3|node|3|node|3|node|3|node|3|node}} {{CDD|node_h1|4|node|3|node_1|3|node|3|node|3|node|3|node|3|node}} |
| bgcolor=#e7dcc3|6-faces | |
| bgcolor=#e7dcc3|5-faces | |
| bgcolor=#e7dcc3|4-faces | |
| bgcolor=#e7dcc3|Cells | |
| bgcolor=#e7dcc3|Faces | |
| bgcolor=#e7dcc3|Edges | |
| bgcolor=#e7dcc3|Vertices | |
| bgcolor=#e7dcc3|Vertex figure | ( )v{ }x{3,3,3,3} |
| bgcolor=#e7dcc3|Coxeter groups | D8, [35,1,1] |
| bgcolor=#e7dcc3|Properties | convex |
In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.
Alternate names
- Truncated demiocteract
- Truncated hemiocteract (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the vertices of a truncated 8-demicube centered at the origin and edge length 6√2 are coordinate permutations:
: (±1,±1,±3,±3,±3,±3,±3,±3)
with an odd number of plus signs.
Images
{{8-demicube Coxeter plane graphs|t01|80}}
Notes
{{reflist}}
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}} [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
- (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)|x3x3o *b3o3o3o3o3o}}
External links
- {{MathWorld|title=Hypercube|urlname=Hypercube}}
- [https://web.archive.org/web/20070310205351/http://members.cox.net/hedrondude/topes.htm Polytopes of Various Dimensions]
- [http://tetraspace.alkaline.org/glossary.htm Multi-dimensional Glossary]
{{Polytopes}}