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Polytopal realizations of finite type \(\mathbf{g}\)-vector fans. (English) Zbl 1382.05075
Summary: This paper shows the polytopality of any finite type \(\mathbf{g}\)-vector fan, acyclic or not. In fact, for any finite Dynkin type \(\Gamma\), we construct a universal associahedron \(\mathsf{Asso}_{\operatorname{un}}(\Gamma)\) with the property that any \(\mathbf{g}\)-vector fan of type {\(\Gamma\)} is the normal fan of a suitable projection of \(\mathsf{Asso}_{\operatorname{un}}(\Gamma)\).

MSC:
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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