Febuary 2020 A new approach to the automorphism group of a platonic surface
David Aulicino
Rocky Mountain J. Math. 50(1): 9-23 (Febuary 2020). DOI: 10.1216/rmj.2020.50.9


We borrow a classical construction from the study of rational billiards in dynamical systems known as the “unfolding construction” and show that it can be used to study the automorphism group of a Platonic surface. More precisely, the monodromy group, or deck group in this case, associated to the cover of a regular polygon or double polygon by the unfolded Platonic surface yields a normal subgroup of the rotation group of the Platonic surface. The quotient of this rotation group by the normal subgroup is always a cyclic group, where explicit bounds on the order of the cyclic group can be given entirely in terms of the Schläfli symbol of the Platonic surface. As a consequence, we provide a new derivation of the rotation groups of the dodecahedron and the Bolza surface.


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David Aulicino. "A new approach to the automorphism group of a platonic surface." Rocky Mountain J. Math. 50 (1) 9 - 23, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.9


Received: 22 May 2019; Revised: 12 August 2019; Accepted: 22 August 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201551
MathSciNet: MR4092541
Digital Object Identifier: 10.1216/rmj.2020.50.9

Primary: 14H37 , 30FXX

Keywords: Platonic surface , regular maps , rotation group

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium


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Vol.50 • No. 1 • Febuary 2020
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