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The '''vertex enumeration problem''' for a [[polyhedron]], a polyhedral [[cell complex]], a [[hyperplane arrangement]], or some other object of [[discrete geometry]], is the problem of determination of the object's [[vertex (geometry)|vertices]] given some formal representation of the object. A classical example is the problem of enumeration of the vertices of a [[convex polyhedron]] specified by the set of linear inequalities:<ref>[[Eric W. Weisstein]] ''CRC Concise Encyclopedia of Mathematic,'' 2002,ISBN 1584883472, p. 3154, article "vertex enumeration"</ref>
:<math>Ax \leq b</math>
where ''A'' is an ''m''×''n'' matrix, ''x'' is an ''n''×1 column vector of variables, and ''b'' is an ''m''×1 column vector of constants.
==Computational complexity==
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