Ehrhart polynomials of lattice polytopes with normalized volumes $5$

TL;DR

This paper classifies all possible $delta$-vectors of lattice polytopes with normalized volume exactly 5, extending previous classifications for volumes up to 4.

Contribution

It provides a complete classification of $delta$-vectors for lattice polytopes with normalized volume 5, filling a gap in the existing volume classifications.

Findings

Complete list of $delta$-vectors for volume 5 polytopes

Extension of previous classifications from volume 4 to 5

New structural insights into lattice polytopes with volume 5

Abstract

A complete classification of the $\delta$-vectors of lattice polytopes whose normalized volumes are at most $4$ is known. In the present paper, we will classify all the $\delta$-vectors of lattice polytopes with normalized volumes $5$.