References

Books

ARM
Peter McMullen and Egon Schulte
Abstract Regular Polytopes (2002)
Macmillan.

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

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

Published papers

C95
Regular maps on non-orientable surfaces    page 1 only
M. Conder & B. Everitt
Geometriae Dedicata, Springer Netherlands (1995) pp. 209-219.       

C96
Asymmetric Combinatorially-Regular Maps
Marston D.E. Conder
Journal of Algebraic Combinatorics 5 (1996) pp. 323-328.

C01
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.

C09
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

L02
Cantankerous Regular Maps     PostScript link
Li & Širáň

N07
Maps, Hypermaps and Related Topics     PDF
Roman Nedela, 2007.

S59
The regular maps on a surface of genus three
F.A.Sherk, 1959
Canad. J. Math. 11, 1959, pp. 452-480.

S86
Topological chirality of certain molecules
J. Simon, 1986
Topology 25(2), pp. 229-235.

W79
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.

W89
Cantankerous maps and rotary embedding of K_n
Stephen E. Wilson, 1989
Journal of Combinatorial Theory, series B vol. 37 pp 262-273.
      Defines "cantankerous".

W09
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).

Z09
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.

Movies

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
Cantellation
Möbius-Kantor graph
Petrie polygon
Regular map
Uniform polyhedron