Talk:Coxeter notation

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)

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)

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)