# Eberhard-type theorems with two kinds of polygons

## TL;DR

This paper extends Eberhard-type theorems by allowing two types of polygons and one vertex type, advancing the understanding of polytope realizability with multiple polygonal face types.

## Contribution

It introduces new Eberhard-type theorems accommodating two polygon types and one vertex type, moving towards a comprehensive classification.

## Key findings

- New theorems for polytope realizability with two polygon types
- Progress towards classifying Eberhard-type results
- Insights into face and vertex configurations in polyhedral maps

## Abstract

Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new theorems of Eberhard-type where we allow adding two kinds of polygons and one type of vertices. We also hint towards a full classification of these types of results.