Talk:Coxeter group
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Possible improvements:
- Describe dihedral groups explicitly as finite Coxeter groups in the Euclidean plane, and explain the geometric meaning of the relator.
- Describe the way in which the symmetric group Sn acts by reflections in Euclidean n-space.
- State the theorem on special subgroups: each subset of the generators generates a subgroup isomorphic to a Coxeter group.
- Say the exact manner in which the group acts by affine reflections: the "geometric representation".
- Give the exact list of which Coxeter groups act discretely by isometric reflections in Euclidean space of some dimension. This list is not too much more complicated than the list of finite Coxeter groups.
- Explain how some Coxeter groups (such as certain triangle groups) act discretely in hyperbolic space of some dimension, generated by isometric reflections.
--Mosher 10:48, 8 October 2005 (UTC)
