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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