Gosset 3 21 polytope

Gosset 3 21 polytope

In 7-dimensional geometry, the 321 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. Coxeter named it 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 rings in this Coxeter-Dynkin diagram: :

This polytope, along with the 7-simplex, can tessellate 7-dimensional space, represented by 331 and Coxeter-Dynkin diagram::.

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] See p342 (figure 3.7c) by Peter mcMullen: (18-gonal node-edge graph of 321)

See also

* 7-polytope
*Semiregular k 21 polytope
*Gosset 1 32 polytope
*Gosset 2 31 polytope


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Gosset 4 21 polytope — The Gosset 421 polytope is an 8 dimensional semiregular uniform polytope composed of 17,280 7 simplex and 2,160 7 orthoplex facets.It was discovered by Thorold Gosset, who described it in his 1900 paper as an 8 ic semi regular figure. It is the… …   Wikipedia

  • Gosset 1 42 polytope — In 8 dimensional geometry, 142 is a uniform polytope, constructed from the E8 group. It is named by Coxeter as 142 by its bifurcating Coxeter Dynkin diagram, with a single ring on the end of the 2 node sequence. It is related to the 421 polytope …   Wikipedia

  • 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 …   Wikipedia

  • 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… …   Wikipedia

  • Gosset 2 41 polytope — In 8 dimensional geometry, 241 is a uniform polytope, constructed from the E8 group. It is named by Coxeter as 241 by its bifurcating Coxeter Dynkin diagram, with a single ring on the end of the 2 node sequence. It is related to the 421 polytope …   Wikipedia

  • Gosset 2 31 polytope — In 7 dimensional geometry, 231 is a uniform polytope, constructed from the E7 group. It is named by Coxeter as 231 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 …   Wikipedia

  • Gosset 1 22 polytope — In 6 dimensional geometry, the 122 polytope is a uniform polytope, related to the 221 polytope, also constructed from the E6 group. It is named by Coxeter as 122 by its bifurcating Coxeter Dynkin diagram, with a single ring on the end of the 1… …   Wikipedia

  • Polytope — Not to be confused with polytrope. In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions, a polyhedron in three dimensions, and so on… …   Wikipedia

  • Polytope — Un polytope en dimension 3 Le terme polytope admet plusieurs définitions au sein des mathématiques. Principalement car les usages diffèrent en quelques points selon les pays, mais l usage américain ayant tendance à s imposer, on se retrouve… …   Wikipédia en Français

  • Gosset 3 31 honeycomb — In 8 dimensional geometry, the 331 honeycomb is a uniform honeycomb, also given by Schlafli symbol {33,3,1}.It has a 231 polytope vertex figure, and is composed of 231 and 7 simplex facets, with 56 and 576 of them respectively around each… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”