Geometriae Dedicata

, Volume 56, Issue 2, pp 209–219 | Cite as

Regular maps on non-orientable surfaces

  • Marston Conder
  • Brent Everitt
Article

Abstract

It is well known that regular maps exist on the projective plane but not on the Klein bottle, nor the non-orientable surface of genus 3. In this paper several infinite families of regular maps are constructed to show that such maps exist on non-orientable surfaces of over 77 per cent of all possible genera.

Mathematics Subject Classification (1991)

05C25 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Biggs, N. L. and White, A. T.:Permutation Groups and Combinatorial Structures, L.M.S. Lecture Note Series, vol. 33, Cambridge University Press, 1979.Google Scholar
  2. 2.
    Cannon, J. J.: An introduction to the group theory language CAYLEY, in M. Atkinson (ed.),Computational Group Theory, Academic Press, San Diego, London, 1984, pp. 145–183.Google Scholar
  3. 3.
    Coxeter, H. S. M.: The abstract groupsG m,n,p,Trans. Amer. Math. Soc. 45 (1939), 73–150.Google Scholar
  4. 4.
    Coxeter, H. S. M. and Moser, W. O. J.:Generators and Relations for Discrete Groups, 4th edn, Springer-Verlag, Berlin, 1980.Google Scholar
  5. 5.
    Wilson, S. E.: Operators over regular maps,Pacific J. Math. 81 (1979), 559–568.Google Scholar
  6. 6.
    Wilson, S. E.: Cantankerous maps and rotary embeddings ofK n,J. Combin. Theory Series B 47 (1989), 262–273.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Marston Conder
    • 1
  • Brent Everitt
    • 1
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Personalised recommendations