# On the lattice Hadwiger number of superballs and some other bodies

## TL;DR

This paper proves that the lattice Hadwiger number of superballs and certain convex bodies grows exponentially with the dimension, highlighting significant complexity in high-dimensional geometric packings.

## Contribution

It establishes the exponential growth of the lattice Hadwiger number for superballs and some convex bodies, advancing understanding of high-dimensional convex geometry.

## Key findings

- Lattice Hadwiger number of superballs is exponential in dimension
- Exponential growth also applies to some other convex bodies
- Highlights complexity in high-dimensional geometric packings

## Abstract

We show that the lattice Hadwiger number of superballs is exponential in the dimension. The same is true for some more general convex bodies.