  We investigate the relationships between the Lipschitz outer geometry and the
embedded topological type of a hypersurface germ in $(\mathbb C^n,0)$. It is
well known that the Lipschitz outer geometry of a complex plane curve germ
determines and is determined by its embedded topological type. We prove that
this does not remain true in higher dimensions. Namely, we give two normal
hypersurface germs $(X_1,0)$ and $(X_2,0)$ in $(\mathbb C^3,0)$ having the same
outer Lipschitz geometry and different embedded topological types. Our pair
consist of two superisolated singularities whose tangent cones form an
Alexander-Zariski pair having only cusp-singularities. Our result is based on a
description of the Lipschitz outer geometry of a superisolated singularity. We
also prove that the Lipschitz inner geometry of a superisolated singularity is
completely determined by its (non embedded) topological type, or equivalently
by the combinatorial type of its tangent cone.
