Discrete & Computational Geometry
We present an algorithm for the classification of triples of lattice polytopes with a given mixed volumemin dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number of which is finite for fixed m. Following this algorithm, we enumerate all irreducible triples of normalized mixed volume up to 4 that are inclusion-maximal. This produces a classification of generic trivariate sparse polynomial systems with up to 4 solutions in the complex torus, up to monomial changes of variables. By a recent result of Esterov, this leads to a description of all generic trivariate sparse polynomial systems that are solvable by radicals.
Averkov, Gennadiy; Borger, Christopher; and Soprunov, Ivan, "Classification of Triples of Lattice Polytopes with a Given Mixed Volume" (2020). Mathematics Faculty Publications. 338.
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