Regular self-dual and self-Petrie-dual maps of arbitrary valency

Jay Fraser, Olivia Jeans, Jozef Širáň


The existence of a regular, self-dual and self-Petrie-dual map of any given even valency has been proved by D. Archdeacon, M. Conder and J. Širáň (2014). In this paper we extend this result to any odd valency ≥ 5. This is done using algebraic number theory and maps defined on the groups PSL(2, p) in the case of odd prime valency ≥ 5 and valency 9, and using coverings for the remaining odd valencies.


Regular map, automorphism group, self-dual map, self-Petrie-dual map

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ISSN: 1855-3974

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