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 isometric copies of a given simplex $A$ (namely, by the alcoves of $\Sigma$). I would like to know what the isometry type of $A$ is, depending on $\widetilde{X}_n$ (at least for the classical types $\widetilde{A}_n$, $\widetilde{B}_n$, $\widetilde{C}_n$ and $\widetilde{D}_n$).

More specifically, if $1$ is the length of the shortest edge of $A$, what are the other possible lengths for the edges of $A$?

(For instance, in type $\widetilde{A}_n$, all edges have length $1$).

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 isometric copies of a given simplex $A$ (namely, by the alcoves of $\Sigma$). I would like to know what the isometry type of $A$ is, depending on $\widetilde{X}_n$ (at least for the classical types $\widetilde{A}_n$, $\widetilde{B}_n$, $\widetilde{C}_n$ and $\widetilde{D}_n$).

More specifically, if $1$ is the length of the shortest edge of $A$, what are the other possible lengths for the edges of $A$?

(For instance, in type $\widetilde{A}_2$, all edges have length $1$).