Séminaire Lotharingien de Combinatoire, B73a (2015), 11 pp.

Paola Cellini and Mario Marietti

Polar Root Polytopes that are Zonotopes

Abstract. Let P\Phi be the root polytope of a finite irreducible crystallographic root system \Phi, i.e., the convex hull of all roots in \Phi. The polar of P\Phi, denoted P\Phi*, coincides with the union of the orbit of the fundamental alcove under the action of the Weyl group. In this paper, we determine which polytopes P\Phi* are zonotopes and which are not. The proof is constructive.

Received: September 10, 2014. Revised: February 6, 2015. Accepted: February 16, 2015.

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