Talk:Coxeter notation

The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.

Mathematics Low‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Low	This article has been rated as Low-priority on the project's priority scale.

Polyhedra

	This article is within the scope of WikiProject Polyhedra, a collaborative effort to improve the coverage of polygons, polyhedra, and other polytopes on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PolyhedraWikipedia:WikiProject PolyhedraTemplate:WikiProject PolyhedraPolyhedra
???	This article has not yet received a rating on the project's importance scale.

Start

I've been using Norman Johnson's preprint Geometries and Transformations, ch 11-13 to construct this article, but just a start so far! Tom Ruen (talk) 02:39, 28 June 2011 (UTC)[reply]

direct subgroup

What does "direct subgroup" mean? I cannot find definition. Is is something like normal subgroup? Or, even more strictly - if G = A x B (direct product), A and B each, are direct subgroups?

Thank you Bor75 (talk) 08:34, 14 December 2011 (UTC)[reply]

A direct subgroup (of a Coxeter group) is one which removes all of the mirrors so only rotational or translation symmetry remains, like [3,3] --> [3,3]⁺, the generators {0,1,2} become {01,12}. A semidirect subgroup only removes some of the reflections, like [3,4] --> [3⁺,4], the generators {0,1,2} become {01,2}. A halving subgroup removes half of the mirrors around one point, like [3,4] --> [3,4,1⁺] = [3,3], the generators {0,1,2} become {0,1,212}. Tom Ruen (talk) 08:13, 13 October 2014 (UTC)[reply]