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E6 polytope
E6 polytope, Vertexedge graph (*)
E6 polytope  

Type  Uniform 6polytope 
Family  Semiregular Epolytope 
SchlĂ¤fli symbol  t_{0}{3^{2,2,1}} 
CoxeterDynkin diagram 

5faces  99 total: 27 pentacrosses and 72 5simplices 
4faces  648 pentachorons 
Cells  1080 tetrahedrons 
Faces  720 triangles 
Edges  216 
Vertices  27 
Vertex figure  demipenteract: {3^{1,2,1}} 
Symmetry group  E_{6}, [3^{2,2,1}] 
Properties  convex 
The E6 polytope is a semiregular polytope, discovered by Thorold Gosset, published in his 1900 paper. He called it an 6ic semiregular figure
Its construction is based on the E6 group. It is also named by Coxeter as 221 by its bifurcating CoxeterDynkin diagram, with a single ring on the end of one of the 2node sequence.
It is also one of a family of 39 convex uniform polytopes in 6dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of ringed CoxeterDynkin diagrams.
See also
* 6polytope
* Semiregular Epolytope
References
* T. Gosset: On the Regular and SemiRegular 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
* Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036 [1]
o (Paper 17) Coxeter, The Evolution of CoxeterDynkin diagrams, [Nieuw Archief voor Wiskunde 9 (1991) 233248] See figure 1: (p.232) (Nodeedge graph of polytope)
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