Vertex Enumeration

A Convex Polyhedron is defined as the set of solutions to a system of linear inequalities

$${\hbox{\sf m}}{\bf x} \leq {\bf b},$$

where ${\hbox{\sf m}}$ is a Real $s\times d$ Matrix and ${\bf b}$ is a Real $s$-Vector. Given ${\hbox{\sf m}}$ and ${\bf b}$, vertex enumeration is the determination of the polyhedron's Vertices.

See also Convex Polyhedron, Polyhedron

References

Avis, D. and Fukuda, K. ``A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra.'' In Proceedings of the 7th ACM Symposium on Computational Geometry, North Conway, NH, 1991, pp. 98-104, 1991.

Fukada, K. and Mizukosh, I. ``Vertex Enumeration Package for Convex Polytopes and Arrangements, Version 0.41 Beta.'' http://www.mathsource.com/cgi-bin/MathSource/Applications/Mathematics/0202-633.