The Steinberg torus of a Weyl group
For a Weyl group W, the Steinberg torus is a simplicial torus obtained by taking the quotient of the affine Coxeter complex by its coroot lattice. A preprint, joint with Kevin Dilks and John Stembridge, can be found on my publications page. Also, slides from a talk on the subject can be found here.
Below are visualizations of the rank 2 and 3 cases.