Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polar Root Polytopes that are Zonotopes   Let $\mathcal P_{\Phi}$ 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 $\mathcal P_{\Phi}$, denoted $\mathcal P_{\Phi}^*$,
coincides with the union of the orbit of the fundamental alcove under the
action of the Weyl group. In this paper, we establishes which polytopes
$\mathcal P_{\Phi}^*$ are zonotopes and which are not. The proof is
constructive.

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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex