A generalization of Filliman duality

Details A generalization of Filliman duality A generalization of Filliman duality

2001-12-07

arxiv.org/abs/math/0112066v3

Mathematics

Metric Geometry

4 pages, 4 figures. Only change in this version is an added reference

Scientific paper

Filliman duality expresses (the characteristic measure of) a convex polytope P containing the origin as an alternating sum of simplices that share supporting hyperplanes with P. The terms in the alternating sum are given by a triangulation of the polar body P^o. The duality can lead to useful formulas for the volume of P. A limiting case called Lawrence's algorithm can be used to compute the Fourier transform of P. 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 P is a convex polytope containing the origin, any realization of P^o as a linear combination of simplices leads to a dual realization of P.

Affiliated with

Also associated with

No associations

Rating

A generalization of Filliman duality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A generalization of Filliman duality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A generalization of Filliman duality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-326142