On Lipschitz normally embedded complex surface germs

We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. prove in particular that the topological type such germ determines combinatorics its minimal resolution which factors through blowup maximal ideal and Nash transform, as well polar curve discriminant generic plane projection, thus generalizing results Spivakovsky Bondil were known for singularities. In an appendix, we give new example singularity.