# Petrie Duality and the Anstee–Robertson Graph

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## Abstract

**:**

## 1. Introduction

## 2. The Petrie Dual of a Map

## 3. The Group of Map Operations

## 4. Maps and Permutations

## 5. Operations and Automorphisms

## 6. The Graph $\mathcal{R}$ and Its Group G

**Lemma 1.**

## 7. Construction of the Maps

**Theorem 2.**

**Corollary 3.**

**Remark**

## 8. Quotient Maps

## 9. Maps and Triangle Groups

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References and Notes

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Jones, G.A.; Ziv-Av, M.
Petrie Duality and the Anstee–Robertson Graph. *Symmetry* **2015**, *7*, 2206-2223.
https://doi.org/10.3390/sym7042206

**AMA Style**

Jones GA, Ziv-Av M.
Petrie Duality and the Anstee–Robertson Graph. *Symmetry*. 2015; 7(4):2206-2223.
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**Chicago/Turabian Style**

Jones, Gareth A., and Matan Ziv-Av.
2015. "Petrie Duality and the Anstee–Robertson Graph" *Symmetry* 7, no. 4: 2206-2223.
https://doi.org/10.3390/sym7042206