# Topology of the icosidodecahedral arrangement

## TL;DR

This paper proves that the icosidodecahedral arrangement is a $K(ty,1)$ space, establishing its topological properties and implications for its Milnor fiber, which was previously known to have torsion in homology.

## Contribution

It demonstrates that the icosidodecahedral arrangement is a $K(ty,1)$ space, providing new insights into its topological structure and properties of its Milnor fiber.

## Key findings

- The icosidodecahedral arrangement is a $K(ty,1)$ space.
- Its Milnor fiber is also a $K(ty,1)$ space.
- The arrangement's homology has torsion in the first integral homology.

## Abstract

The icosidodecahedral arrangement is introduced by M. Yoshinaga (arXiv:1902.06256) as the first known example that is a hyperplane arrangement whose Milnor fiber has torsions in first integral homology. In this note, we prove that the icosidodecahedral arrangement is $K(\pi,1)$, hence so is its Milnor fiber.