# Intersecting hexagons in 3-space

## TL;DR

This paper investigates the combinatorial geometry of hexagons in three-dimensional space, establishing that the maximum number of 'fat' hexagons on n points without heavy intersections grows slower than quadratically with n.

## Contribution

It introduces the concept of heavy intersection for hexagons in 3D and proves a bound on their maximum number under certain geometric conditions.

## Key findings

- Number of heavy-intersection-free fat hexagons is o(n^2)
- Heavy intersections are constrained in 3D configurations
- Provides bounds for geometric arrangements of hexagons

## Abstract

Two hexagons in the space are said to intersect heavily if their intersection consists of at least one common vertex as well as an interior point. We show that the number of hexagons on n points in 3-space without heavy intersections is o(n^2), under the assumption that the hexagons are "fat".