Classification of lattice polytopes with small volumes

DOI10.4310/JOC.2020.V11.N3.A4arXiv1708.00413MaRDI QIDQ6289651

Akiyoshi Tsuchiya, Takayuki Hibi

Publication date: 1 August 2017

Abstract: In the frame of a classification of general square systems of polynomial equations solvable by radicals, Esterov and Gusev succeeded in classifying all spanning lattice polytopes whose normalized volumes are at most $4$. In the present paper, we complete to classify all lattice polytopes whose normalized volumes are at most $4$ based on the known classification of their $delta$-polynomials.

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20)

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