Classification of lattice polytopes with small volumes

TL;DR

This paper completes the classification of lattice polytopes with normalized volumes up to 4, building on previous work and utilizing known classifications of their δ-polynomials to achieve a comprehensive understanding.

Contribution

It provides a complete classification of all lattice polytopes with normalized volume at most 4, extending prior partial classifications using δ-polynomial analysis.

Findings

Complete classification of lattice polytopes with volume ≤ 4

Utilizes δ-polynomial classification methods

Builds on previous work by Esterov and Gusev

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.