Canonical form of a convex polytope via its dual volume

The main goal of this talk is to introduce a method to compute the canonical form of a convex polytope by computing the volume of its polar dual polytope. We will first define the notion of a dual polytope and then compute the volume in a concrete example. Then we will give a proof that the dual volume actually gives the canonical form of the original convex polytope. Finally, we will introduce a more efficient way to compute the dual volume when the polytope has many vertices but few sides, via the Filliman Duality, which roughly says the volume of the polytope can be obtained from triangulating its dual.

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Date published: Wednesday, November 29, 2023