E7 polytope
From Wikipedia, the free encyclopedia
| E7 polytope | |
|---|---|
 Vertex-edge graph |
|
| Type | Uniform 7-polytope |
| Family | Semiregular E-polytope |
| Schläfli symbol | t0{33,2,1} |
| Coxeter-Dynkin diagram |     |
| 6-faces | 702 total: 126 hexacrosses and 576 6-simplices |
| 5-faces | 6048 5-simplices |
| 4-faces | 12096 pentachorons |
| Cells | 10080 tetrahedrons |
| Faces | 4032 triangles |
| Edges | 756 |
| Vertices | 56 |
| Vertex figure | E6 polytope: {32,2,1} |
| Symmetry group | E7, [33,2,1] |
| Properties | convex |
The E7 polytope is a semiregular polytope, enumerated by Thorold Gosset in his 1900 paper. He called it an 7-ic semi-regular figure. It is called the Hess polytope for Edmund Hess who first discovered it.
Its construction is based on the E7 group. It is also named by Coxeter as 321 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 3-node sequence.
It is also one of a family of 127 (27-1) convex uniform polytopes in 7-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of ringed Coxeter-Dynkin diagrams.
[edit] References
- T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900
- A. Boole Stott: Geometrical deduction of semiregular from regular polytopes and space fillings, Verhandelingen of the Koninklijke academy van Wetenschappen width unit Amsterdam, Eerste Sectie 11,1, Amsterdam, 1910
- 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 [1]
- (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45] See p342 (figure 3.7c) by Peter mcMullen: (18-gonal node-edge graph of 321)
[edit] See also
 |
This geometry-related article is a stub. You can help Wikipedia by expanding it. |
