Zhongyuan Liu

collaborators

2 papers

math.MG2025

Kissing polytopes in dimension 3

Antoine Deza, Zhongyuan Liu, Lionel Pournin

It is shown that the smallest possible distance between two disjoint lattice polytopes contained in the cube $[0, k]^{3}$ is exactly $\frac{1}{2 ( 2 k ^{2} - 4 k + 5 ) ( 2 k ^{2} - 2 k + 1 )}$ for…

math.CO2024

Small kissing polytopes

Antoine Deza, Zhongyuan Liu, Lionel Pournin

A lattice $(d, k)$ -polytope is the convex hull of a set of points in $R^{d}$ whose coordinates are integers ranging between $0$ and $k$ . We consider the smallest possible dis…