# Diameter two properties and polyhedrality

## TL;DR

This paper presents examples of polyhedral Banach spaces that do not exhibit diameter two properties, demonstrating that polyhedrality is not necessarily related to these properties.

## Contribution

It provides the first known examples showing the lack of connection between polyhedrality and diameter two properties in Banach spaces.

## Key findings

- Polyhedral Banach spaces can lack diameter two properties.
- Examples challenge previous assumptions about their relationship.
- Highlights the independence of polyhedrality from diameter two properties.

## Abstract

We give two examples of polyhedral Banach spaces failing all the diameter two properties, showing that there is not any connection between polyhedrality and the diameter two properties.