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The Delaunay triangulation maximizes the smallest interior angle.

The Delaunay triangulation of a point set is unique (unless a triangle circumcircle intersects more than 3 vertices).

Dual properties of Delaunay triangulations and Voronoi diagrams

Delauny triangulation	Voronoi diagram
Each triangle circumcircle contains no other vertices in its interior.	Around each Voronoi vertex, there exists a smallest circumcircle touching at least 3 Voronoi sites and containing no sites in its interior.
For every edge, there exists an empty circle containing both endpoints.	For every Voronoi edge, there exists a circle containing both adjacent Voronoi sites but no other sites.