Abstract
The normal fan of a polyhedral convex set in ℝ n is the collection of its normal cones. The structure of the normal fan reflects the geometry of that set. This paper reviews and studies properties about the normal fan. In particular, it investigates situations in which the normal fan of a polyhedral convex set refines, or is a subfan of, that of another set. It then applies these techniques in several examples. One of these concerns the face structure and normal manifold of the critical cone of a polyhedral convex set associated with a point in ℝ n . Another concerns how perturbation of the right hand side of the linear constraints defining such a set affects the normal fan and the face structure.
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