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Thanks to the theory of Coxeter groups, we produce the first family ofCalabi-Yau manifolds $X$ of arbitrary dimension $n$, for which $\Bir(X)$ isinfinite and the Kawamata-Morrison movable cone conjecture is satisfied. Forthis family, the movable cone is explicitly described; it's fractal nature isrelated to limit sets of Kleinian groups and to the Apollonian Gasket. Then, weproduce explicit examples of (biregular) automorphisms with positive entropy onsome Calabi-Yau manifolds.

Birational automorphism groups and the movable cone theorem for Calabi-Yau manifolds of Wehler type via universal Coxeter groups