References

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

RP
H.S.M.Coxeter
Regular Polytopes
Dover, 1973; ISBN 0-486-61480-8.

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

STA
Hubert Phillips
Something to Think About
Ptarmigan Books, 1945.

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

B71
Automorphisms of Imbedded Graphs
Journal of Combinatorial Theory, 11, 132-138 (1971)
Norman Biggs

B97
Polyhedral Maps    pdf link
U. Brehm & E. Schulte

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    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

G03
Are your polyhedra the same as my polyhedra?    PDF link   
Branko Grünbaum
Discrete and Computational Geometry. The Goodman-Pollack Festschrift.
      Gives many definitions

H01
Dessins d'enfants and Origami curves    PDF link   
Frank Herrlich and Gabriela Schmithüsen
Institut für Algebra und Geometrie, Universität Karlsruhe

J85
Regular Orientable Imbeddings of Complete Graphs
Journal of Combinatorial Theory, series B 39, 353-367 (1985)
Lynne James and Gareth Jones
      Classifies embeddings of complete graphs in orientable surfaces.

J01
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.

J02
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.

J10
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".

K10
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.

L02
Cantankerous Regular Maps     PostScript link
Li & Širáň

N07
Maps, Hypermaps and Related Topics     pdf link
Roman Nedela, 2007.

S94
Dessins d'enfants on the Riemann sphere    PDF link   
Leila Schneps
London math. soc. lecture notes 200, C.U.P., 1994

S10
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.

S13
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

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.

S06
The Grothendieck Theory of Dessins d'Enfants    PDF link   
Vijaykumar Haribansh Singh
Chennai Mathematical Institute: M.Sc. thesis for Madhya Pradesh Bhoj University. 2006

W12
Grothendieck's dessins d'enfants    PDF link   
Milan Werncke
Bachelor thesis, 2012

W79
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.

W85
Cantankerous Maps and Rotary Embeddings of K_n
Journal of Combinatorial Theory, series B 47, 262-273 (1989)
Stephen E. Wilson
      Describes cantankerous maps, and lists those then known.

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 link
Jay Zimmerman, 2009
Bridges 2009: Mathematics, Music, Art, Architecture, Culture
      The group has order 32.

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.

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