1994, David Eppstein, Chapter 10: Average Case Analysis of Dynamic Geometric Optimization, Association of Computing Machinery, Society for Industrial and Applied Mathematics, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, page 83,
This problem can be solved in time O(nᶜ) by combining a weight-balanced tree of the convex hull vertices with a farthest neighbor data structure of Agarwal and Matoušek [2].

Thus, the polyhedron and the convex hull of the set of its vertices coincide, which was to be proved.
Since the convex hull of a set M is determined uniquely from M, Theorem 1 implies that a bounded solid polyhedron and its surface, i.e., a closed convex polyhedron, are determined uniquely from its vertices.

The convex hull of a compact subset of an infinite dimensional topological vector space need not be a compact set.

Convex hull

Meaning

Noun

Synonyms