In mathematics, the 11-cell (or hendecachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 11 cells are hemi-icosahedral. It has 11 vertices, 55 edges and 55 faces. Its symmetry group is the projective special linear group L2(11), so it has660 symmetries. It has Schläfli symbol {3,5,3}.

It was discovered by Branko Grünbaum in 1977, who constructed it by pasting hemi-icosahedra together, three per edge until the shape closed up. It was independently discovered by H. S. M. Coxeter in 1984, who studied its structure and symmetry in greater depth.

The abstract "11-cell" contains the same number of vertices and edges as the 10-dimensional 10-simplex, and contains 1/3 of its 165 faces. Thus it could be drawn as a regular figure in 11-space, although its hemi-icosahedral cells would be skew (Cell vertices are not contained within the same 3 dimensional subspace).

See also

* 57-cell
* Order-3 icosahedral honeycomb - regular honeycomb with same Schläfli symbol {3,5,3}.


* Peter McMullen, Egon Schulte, "Abstract Regular Polytopes", Cambridge University Press, 2002. ISBN 0-521-81496-0
* Coxeter, H.S.M., "A Symmetrical Arrangement of Eleven hemi-Icosahedra", Annals of Discrete Mathematics 20 pp103–114.

External links

* [http://discovermagazine.com/2007/apr/jarons-world-shapes-in-other-dimensions J. Lanier, Jaron’s World. Discover, April 2007, pp 28-29.]
* [http://www.cs.berkeley.edu/~sequin/PAPERS/2007_ISAMA_11Cell.pdf] 2007 ISAMA paper: "Hyperseeing the Regular Hendecachoron", Carlo H. Séquin & Jaron Lanier

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Cell (microprocessor) — Cell is a microprocessor architecture jointly developed by Sony Computer Entertainment, Toshiba, and IBM, an alliance known as STI . The architectural design and first implementation were carried out at the STI Design Center in Austin, Texas over …   Wikipedia

  • Cell culture — in a Petri dish Epithelial cells in culture, stained for keratin (red) an …   Wikipedia

  • Cell — Saltar a navegación, búsqueda Para el personaje de Dragon Ball Z, véase Cell (Dragon Ball). El procesador Cell Cell es una arquitectura de microprocesador desarrollada conjuntamente por Sony Computer Entertainment …   Wikipedia Español

  • Cell signaling — is part of a complex system of communication that governs basic cellular activities and coordinates cell actions. [Witzany, G. (2000). Life: The Communicative Structure. Norderstedt, Libri BoD.] The ability of cells to perceive and correctly… …   Wikipedia

  • Cell (Processeur) — Pour les articles homonymes, voir Cell. Le Cell est un processeur conçu conjointement par IBM, Sony et Toshiba, révélé en février 2005. Il équipe notamment la console de jeu vidéo PlayStation 3 de Sony. Il est envisagé de produire également… …   Wikipédia en Français

  • Cell Jr. — Cell (Dragon Ball) Pour les articles homonymes, voir Cell. Cell Personnage de Dragon Ball …   Wikipédia en Français

  • Cell (Dragon Ball) — Saltar a navegación, búsqueda Cell セル (Seru) Sexo Masculino Fecha de nacimiento Futuro alterno (787), Presente (763 767) Origen en manga …   Wikipedia Español

  • Cell theory — refers to the idea that cells are the basic unit of structure in every living thing. Development of this theory during the Mid 1600s was made possible by advances in microscopy. This theory is one of the foundations of biology. The theory says… …   Wikipedia

  • Cell site — Cell phone tower in Palatine, Illinois, USA. A short mast cell site o …   Wikipedia

  • Cell disruption — is a method or process for releasing biological molecules from inside a cell. Choice of disruption method The production of biologically interesting molecules using cloning and culturing methods allows the study and manufacture of relevant… …   Wikipedia

  • Cell migration — is a central process in the development and maintenance of multicellular organisms. Tissue formation during embryonic development, wound healing and immune responses all require the orchestrated movement of cells in a particular direction to a… …   Wikipedia

Share the article and excerpts

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

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.