# Polyhedral cone

A **polyhedral cone** is a convex cone with a finite number of extreme rays.

## Definition

Ziegler defines a polyhedral cone cone(*Y*) as the set of all linear combinations with nonnegative coefficients of a finite set of vectors Y .^{[1]} In the case of the empty set, we define .

Equivalently, a polyhedral cone can be defined as the convex hull of the origin and a finite set of rays extending from the origin.

Grunbaum^{[2]} generalizes this definition to allow an apex other than the origin, notated where a is the apex. Otherwise, the definition is the same.

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