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Questions about the branch of algebra that deals with groups.
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Isometry type of alcoves in affine Coxeter complexes
Let $W$ be an irreducible affine Coxeter group (say of type $\widetilde{X}_n$), and let $\Sigma$ be the associated Coxeter complex. Thus, $\Sigma$ is an $n$-dimensional Euclidean space tesselated by i …