On the densest packing of polycylinders in any dimension

TL;DR

This paper proves that the densest packing of polycylinders in any dimension achieves a density of π/√12, extending previous results through geometric and dimension reduction techniques.

Contribution

It applies transversality and dimension reduction methods to establish the optimal packing density of polycylinders in all dimensions, generalizing prior work.

Findings

Optimal packing density of polycylinders is π/√12 in all dimensions.

Extension of previous results to higher dimensions.

Use of geometric and dimension reduction techniques.

Abstract

Using transversality and a dimension reduction argument, a result of A. Bezdek and W. Kuperberg is applied to polycylinders $\mathbb{D}^2\times \mathbb{R}^n$, showing that the optimal packing density is $\pi/\sqrt{12}$ in any dimension.