# Dual billiards, Fagnano orbits and regular polygons

## TL;DR

This paper investigates Fagnano orbits in dual polygonal billiards to characterize regular polygons and analyzes the iteration of the developing map.

## Contribution

It introduces the concept of Fagnano orbits for dual billiards and uses them to uniquely identify regular polygons.

## Key findings

- Fagnano orbits characterize regular polygons.
- Analysis of the developing map's iteration.
- New insights into dual billiard dynamics.

## Abstract

We study the notion of Fagnano orbits for dual polygonal billiards. We used them to characterize regular polygons and we study the iteration of the developing map.