Talk:Coxeter element

Geometric folding

Example use: This is a 3D model of the 4₂₁ from E8, apparently projected into 4D of (H4), and then one dimension removed.

Mathematical representation of the physical Zome model isomorphic (?) to E8. This is constructed from my VisibLie_E8 tool using two concentric 600 Cells (at the golden ratio) with orthogonal projections to 3D. Jgmoxness (talk)

I'm not sure where this belongs, under Coxeter-Dynkin diagram or Coxeter group or here, but these graphics show symmetric "folding" operations (vertical offsets show equivalent nodes between the graphs), apparently useful for showing projection symmetry of uniform polytopes in lower dimensions. They were extracted from a paper Generalized Dynkin diagrams and root systems and their folding by Jean-Bernard Zuber, 1996. (I ignored the projection of Ak to I₂(k+1) since this was the same as the Coxeter plane projection for the simplex.) Tom Ruen (talk) 14:03, 19 November 2010 (UTC)

Nonuniqueness of Coxeter plane

The 24-cell has two distinct B3/A2 Coxeter planes. Probably has to do with the fact that it has two distinct B3 projections into 3-space. — Preceding unsigned comment added by 98.207.169.109 (talk) 23:08, 16 September 2017 (UTC)

Yes, this is true. They are labeled as (a) and (b) here 24-cell#Orthogonal_projections. Tom Ruen (talk) 04:18, 17 September 2017 (UTC)

two Ps in this pod is a crowd

For a given Coxeter element w, there is a unique plane P on which w acts by rotation by 2π/h. This is called the Coxeter plane and is the plane on which P has eigenvalues e^2πi/h and e^−2πi/h = e^{2πi(h−1)/h}.

If the second P is distinct from the first P, a definition would be helpful. If they're the same, wouldn't you expect every plane to have the same eigenvalues on itself? —Tamfang (talk) 06:01, 2 May 2018 (UTC)

What is it, anyway?

In an article titled Coxeter element, how about a simple example of a Coxeter element to go along with the extensive tables of everything else? What, for example, is a Coxeter element of the polygon group [n]? —Tamfang (talk) 06:04, 2 May 2018 (UTC)

Element or number

The titel is 'Coxeter element', but the article defines the 'Coxeter number'. And as far as I can see, nowhere in the article is a clear definition of Coxeter element. Madyno (talk) 22:36, 2 February 2020 (UTC)