Gosset 2 21 polytope

In 6-dimensional geometry, 2₂₁ 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. Coxeter named it 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 rings in this Coxeter-Dynkin diagram: :

This polytope can tessellate 6-dimensional space, represented by the symbol, 2₂₂, and Coxeter-Dynkin diagram .

See also

* 6-polytope
*Semiregular k₂₁ polytope
* 1_k2 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 [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471010030.html]
** (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)