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E6 polytope, Vertex-edge graph (*)

E6 polytope
Type Uniform 6-polytope
Family Semiregular E-polytope
Schläfli symbol t0{32,2,1}
Coxeter-Dynkin diagram
5-faces 99 total:
27 pentacrosses and
72 5-simplices
4-faces 648 pentachorons
Cells 1080 tetrahedrons
Faces 720 triangles
Edges 216
Vertices 27
Vertex figure demipenteract: {31,2,1}
Symmetry group E6, [32,2,1]
Properties convex

The E6 polytope is a semiregular polytope, discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure

Its construction is based on the E6 group. It is also named by Coxeter as 221 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequence.

It is also one of a family of 39 convex uniform polytopes in 6-dimensions, made of uniform polytope facets and vertex figures, defined by all permutations of ringed Coxeter-Dynkin diagrams.

See also

* 6-polytope

* Semiregular E-polytope

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

* 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]

o (Paper 17) Coxeter, The Evolution of Coxeter-Dynkin diagrams, [Nieuw Archief voor Wiskunde 9 (1991) 233-248] See figure 1: (p.232) (Node-edge graph of polytope)

Geometry

Mathematics Encyclopedia

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