Regular maps and hypermaps of Euler characteristic -1 to -200

  • Authors:

  • Marston D. E. Conder

  • Affiliations:

  • Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2009

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Abstract

This paper describes the determination of all orientably-regular maps and hypermaps of genus 2 to 101, and all non-orientable regular maps and hypermaps of genus 3 to 202. It extends the lists obtained by Conder and Dobcsanyi (2001) of all such maps of Euler characteristic -1 to -28, and corrects errors made in those lists for the vertex- or face-multiplicities of 14 'cantankerous' non-orientable regular maps. Also some discoveries are announced about the genus spectrum of orientably-regular but chiral maps, and the genus spectrum of orientably-regular maps having no multiple edges, made possible by observations of patterns in the extension of these lists to higher genera.