# Hunting for reduced polytopes

## TL;DR

This paper demonstrates the existence of reduced polytopes in three-dimensional space and introduces a new necessary condition, advancing understanding of their properties in higher dimensions.

## Contribution

It provides the first known example of reduced polytopes in 3D and establishes a novel necessary condition for their existence.

## Key findings

- Existence of reduced polytopes in 3D confirmed
- A new necessary condition for 3D reduced polytopes established
- Partially answers Lassak's question on higher-dimensional reduced polytopes

## Abstract

We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in $d$-dimensional Euclidean space for $d\geq 3$. Moreover, we prove a novel necessary condition on reduced polytopes in three-dimensional Euclidean space.