| Abstract: | Filliman duality expresses (the characteristic measure of) a convex polytope  containing the origin as an alternating sum of simplices that share supporting hyperplanes with  . The terms in the alternating sum are given by a triangulation of the polar body  . The duality can lead to useful formulas for the volume of  . A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of  . In this note we extend Filliman duality to an involution on the space of polytopal measures on a finite-dimensional vector space, excluding polytopes that have a supporting hyperplane coplanar with the origin. As a special case, if  is a convex polytope containing the origin, any realization of  as a linear combination of simplices leads to a dual realization of  . |
