Extreme Vertex:

A vertex v of a polyhedral surface M is called a local extreme vertex if v is a vertex of the convex hull of the star of v, and it is a (global) extreme vertex if it is a vertex of the convex hull of M.

A local extreme vertex is the local maximum for the height function on M in some direction, and a vertex that is not locally extreme is a saddle point for every height function on M.

The extreme vertices can be used as a convenient means of describing tightness for polyhedral surfaces. [More]

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