The Coxeter complex has faces represented by cosets of standard parabolic subgroups, ordered by reverse inclusion. Geometrically, its maximal simplices are the chambers of the Coxeter arrangement intersected with a sphere.
The Coxeter complex is a mathematical concept that arises in the field of geometry and combinatorial group theory. It is closely associated with Coxeter groups, which are groups generated by reflections across hyperplanes in a Euclidean space. The Coxeter complex provides a way to visualize the geometric structure related to these groups.
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