Rotary Hypermaps of Genus 2

Abstract

We classify the rotary hypermaps (sometimes called regular hypermaps) on an orientable surface of genus 2. There are 43 of them, of which 10 are maps (classified by Threlfall), 20 more can be obtained from the 10 maps by applying Machì’s operations, and the remaining 13 may be obtained from the maps by using Walsh’s bijection between maps and hypermaps. As a corollary, we deduce that there are no non-orientable reflexible hypermaps of characteristic −1

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Last time updated on 23/10/2014

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