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