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Vertex Enumeration

A convex polyhedron is defined as the set of solutions to a system of linear inequalities

mx<=b

(i.e., a matrix inequality), where m is a real s×d matrix and b is a real s-vector. Given m and b, vertex enumeration is the determination of the polyhedron's polyhedron vertices.

See also

Computational Geometry, Convex Hull, Convex Polyhedron, Matrix Inequality, Polyhedron

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References

Avis, D. and Fukuda, K. "A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra." In ACM Symposium on Computational Geometry. Papers from the Seventh Annual Symposium held in North Conway, New Hampshire, June 10-12, 1991 (Ed. H. Edelsbrunner). Disc. Comput. Geom. 8, 295-313, 1992. Fukada, K. and Mizukosh, I. "Vertex Enumeration Package for Convex Polytopes and Arrangements." http://library.wolfram.com/infocenter/MathSource/440/.

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Vertex Enumeration

Cite this as:

Weisstein, Eric W. "Vertex Enumeration." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/VertexEnumeration.html

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