Gosset 1 42 polytope

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, discovered by Thorold Gosset in 1900.

It is also one of a family of 255 (28 − 1) convex uniform polytopes in 8-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 demiocteract, can tessellate 8-dimensional space, represented by the symbol 152, and Coxeter-Dynkin diagram::

See also

* E8 (mathematics)
* 8-polytope
*Semiregular k21 polytope
*421 polytope
*241 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]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • 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… …   Wikipedia

  • 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 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”