Gosset 1 32 polytope

Gosset 1 32 polytope

In 7-dimensional geometry, 132 is a uniform polytope, constructed from the E7 group. It is named by Coxeter as 132 by its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequence. It is related to the 321 polytope, discovered by Thorold Gosset in 1900.

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 rings in this Coxeter-Dynkin diagram::

This polytope can tessellate 7-dimensional space, with symbol 133, and Coxeter-Dynkin diagram::.

See also

*Semiregular k21 polytope
*321 polytope
*231 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
** 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 24) H.S.M. Coxeter, "Regular and Semi-Regular Polytopes III", [Math. Zeit. 200 (1988) 3-45]


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