Index:   books | published papers | web pages | movies | Wikipedia articles


Peter McMullen and Egon Schulte
Abstract Regular Polytopes
Cambridge University Press, 2002; ISBN 0-521-81496-0.

Regular Polytopes
Dover, 1973; ISBN 0-486-61480-8.

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

Hubert Phillips
Something to Think About
Ptarmigan Books, 1945.

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

Published papers

Polyhedral Maps    pdf link
U. Brehm & E. Schulte

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    Postscript 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

Are your polyhedra the same as my polyhedra?    PDF link   
Branko Grünbaum
Discrete and Computational Geometry. The Goodman-Pollack Festschrift.
      Gives many definitions

Dessins d'enfants and Origami curves    PDF link   
Frank Herrlich and Gabriela Schmithüsen
Institut für Algebra und Geometrie, Universität Karlsruhe

Maps on surfaces and Galois groups PDF link
Gareth A. Jones
Mathematica Slovaka, Vol. 97 (1997), No. 1, 1-33
      About connections between maps on surfaces, permutation groups, Riemann surfaces, algebraic curves, and Galois groups.

Theory of Maps on Orientable Surfaces PDF link for paid subscribers
Gareth A. Jones and David Singerman
Proc. London Math. Soc. (1978) s3-37(2): 273-307
      Properties of a multivariate function, called orbicyclic, that arises in enumerative combinatorics in counting nonisomorphic maps on orientable surfaces.

Maps admitting trialities but not dualities PDF link
Gareth A. Jones and Andrew Poulton
European Journal of Combinatorics (2010) vol.31 no.2 1805-1818
      Shows how to find what these pages call "hexads of size 2".

The Belyi functions and dessin d'enfants corresponding to the nononormal inclusions of triangle groups    PDF link   
Kenji Hoshino
Math. J. Okayama 52 (2010) 45-60.

Cantankerous Regular Maps     PostScript link
Li & Širáň

Maps, Hypermaps and Related Topics     pdf link
Roman Nedela, 2007.

Dessins d'enfants on the Riemann sphere    PDF link   
Leila Schneps
London math. soc. lecture notes 200, C.U.P., 1994

My Search for Symmetrical Embeddings of Regular Maps    PDF link   
Carlo Séquin
Delivered at Bridges Conference, Pécs, Hungary, July 24-28, 2010, pp 85-94.

Symmetrical Immersions of Low-genus Non-orientable Regular Maps    PDF link   
Carlo Séquin
Culture and Science, 2013
Delivered at Symmetry Festival, Delft, the Netherlands, August 2-7, 2013

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.

The Grothendieck Theory of Dessins d'Enfants    PDF link   
Vijaykumar Haribansh Singh
Chennai Mathematical Institute: M.Sc. thesis for Madhya Pradesh Bhoj University. 2006

Grothendieck's dessins d'enfants    PDF link   
Milan Werncke
Bachelor thesis, 2012

Operators over regular maps    pdf link
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 link
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.

Faniry Razafindrazaka & Konrad Polthier
Regular Surfaces and Regular Maps

David A. Richter
How to Make the Mathieu Group M24
Relates M24, S3:{3,7}, and the small cubicuboctahedron.

Carlo H. Séquin
Patterns on the Genus-3 Klein Quartic
Interesting pictures.

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 21 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

Index to Regular Maps
Glossary for Regular Maps