Peter McMullen and Egon Schulte
Abstract Regular Polytopes (2002)

"Lewis Carroll"
Sylvie and Bruno Concluded (1893)
Cambridge University Press, 2002; ISBN 0-521-81496-0.

Jarke J. van Wijk
Symmetric tiling of closed surfaces: visualization of regular maps
ACM New York, 2009

Published papers

Regular maps on non-orientable surfaces    page 1 only
M. Conder & B. Everitt
Geometriae Dedicata, Springer Netherlands (1995) pp. 209-219.       

Asymmetric Combinatorially-Regular Maps
Marston D.E. Conder
Journal of Algebraic Combinatorics 5 (1996) pp. 323-328.

Determination of all Regular Maps of Small Genus
M. Conder & P. Dobcsányi
Journal of Combinatorial Theory, Series B 81 (2001) pp. 224-242.
      Lists all regular maps up to S15 and C15.

Regular maps and hypermaps of Euler characteristic -1 to -200    html link
Marston D.E. Conder
Journal of Combinatorial Theory, Series B 99 (2009) pp. 455-459.
      corrects errors on C01 above; links to lists below

Cantankerous Regular Maps     PostScript link
Li & Širáň

Maps, Hypermaps and Related Topics     PDF
Roman Nedela, 2007.

The regular maps on a surface of genus three
F.A.Sherk, 1959
Canad. J. Math. 11, 1959, pp. 452-480.

Topological chirality of certain molecules
J. Simon, 1986
Topology 25(2), pp. 229-235.

Operators over regular maps    PDF
Stephen E. Wilson, 1979
Pacific J. Math. Volume 81, No. 2 (1979), 559-568.
      Discuses Petrie duals, and maps derived using holes.

Cantankerous maps and rotary embedding of Kn
Stephen E. Wilson, 1989
Journal of Combinatorial Theory, series B vol. 37 pp 262-273.
      Defines "cantankerous".

Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps    pdf link
Jarke J. van Wijk
Transactions on Graphics vol 28 no. 3 article 49 (2009).

A Group Portrait on a Surface of Genus Five    PDF
Jay Zimmerman, 2009
Bridges 2009: Mathematics, Music, Art, Architecture, Culture
      The group has order 32.

Web pages

Marston Conder
Lists of rotary and regular maps and hypermaps of small genus
Lists everything up to S101 and C201. Supplements C09 above

Greg Egan
Klein's Quartic Curve
Very clearly written. Discusses S3:{7,3}.

Brunko Grünbaum
Are Your Polyhedra the Same as My Polyhedra?
Interested in "noble maps" which are face- and vertex-transitive, but not edge-transitive. Allows vertices or faces to coincide in space.

Roman Nedela
Maps, Hypermaps and Related Topics
Many useful references.

Carlo H. Séquin
Patterns on the Genus-3 Klein Quartic
Interesting pictures, but not reliable.

Carlo H. Séquin and Ling Xiao
K12 and the Genus-6 Tiffany Lamp
Describes S6:{3,11} (12 vertices, 44 faces and 66 edges), S3:{3,8}, and S3:{8,3}.

Gerard Westendorp
Platonic tilings of Riemann surfaces
With pictures of genus-2 {5,4}, also genus-3 {8,3}.

Jarke J. van Wijk
Visualization of Regular Maps
Short, showing only S0:{4,3} and S3:{8,3}. Acts as an introduction to Mo01 below.


Jarke J. van Wijk
Symmetric Tiling of Closed Surfaces: Visualization of Regular Maps
A 56Mb wmv showing 23 orientable regular maps, all drawn on surfaces which are embedded in 3-space and then rotated to display them.

Wikipedia articles

Abstract polytope
Möbius-Kantor graph
Petrie polygon
Regular map
Uniform polyhedron

Some regular maps drawn on orientable 2-manifolds
Some pages on groups