Abstract
This paper explores the metrical properties of convex polytopes by means of the classical Plucker embedding of the GrassmannianG(k, n) ofk-planes inRn into the exterior algebra ?kRn. The results follow from the description of the volume of the projection of a polytope into ak-plane by a piecewise linear function onG(k, n). For example, the Hodge-star operator is used to obtain the volume of a polytope from its Gale transform. Also, the classification of the faces ofG(2,n) (orG(n?2,n)) imply that the largest projection within a particular combinatorial type is unique ifk=2 orn?2.
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