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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\u00a0<jats:italic>m<\/jats:italic>. 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.<\/jats:p>","DOI":"10.1007\/s00454-020-00246-4","type":"journal-article","created":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T16:08:54Z","timestamp":1602605334000},"page":"165-202","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Classification of Triples of Lattice Polytopes with a Given Mixed Volume"],"prefix":"10.1007","volume":"66","author":[{"given":"Gennadiy","family":"Averkov","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9735-394X","authenticated-orcid":false,"given":"Christopher","family":"Borger","sequence":"additional","affiliation":[]},{"given":"Ivan","family":"Soprunov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,13]]},"reference":[{"key":"246_CR1","doi-asserted-by":"crossref","unstructured":"Averkov, G., Borger, C., Soprunov, I.: Classification of triples of lattice polytopes with a given mixed volume (2019). arXiv:1902.00891","DOI":"10.1007\/s00454-020-00246-4"},{"issue":"4","key":"246_CR2","doi-asserted-by":"publisher","first-page":"1003","DOI":"10.1112\/mtk.12055","volume":"66","author":"G Averkov","year":"2020","unstructured":"Averkov, G., Borger, C., Soprunov, I.: Inequalities between mixed volumes of convex bodies: volume bounds for the Minkowski sum. 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