This is the reference section of the document Constructing Semi-Regular Tilings which is based on a talk given at the Spring 1995 Meeting of the Seaway Section of the Mathematical Association of America. The meeting was held at Hobart and William Smith Collleges in Geneva, New York on April 21--22, 1995.

The complete document is divided into five sections:

  1. Introduction and Historical Background
  2. Notation and Definitions
  3. General Theorems
  4. Hyperbolic Results
  5. References

[Ca] C. Caratheodory. Theory of Functions, Vol. II. Chelsea, New York. 1960. Pages 177--182.

[C-M] H. S. M. Coxeter and W. O. J. Moser. Generators and Relations for Discrete Groups. Springer-Verlag. New York. 1980. Pages 52--61.

[Co] H. S. M. Coxeter. "The non-Euclidean symmetry of Escher's picture 'Circle Limit III.'" Leonardo, Vol. 12 . 1979. Pages 19--25.

[D-H] A.W.M.Dress and D.H.Huson. "On tilings of the plane." Geometrae Dedicata, Vol. 24 . 1987 Pages 269--296.

[D1] D. J. Dunham. "Creating hyperbolic Escher patterns." M.C.Escher: Art and Science. H.S.M. Coxeter et al. (Editors). North-Holland. Amsterdam. 1986 Pages 241--248.

[D2] D. J. Dunham. "Hyperbolic symmetry." Computers and Mathematics with Applications, Vol. 12B. Pages 139--153.

[FT] L. Fejes Toth Regular Figures. Pergamon Press. Oxford. 1964.

[G] M. J. Greenberg. Euclidean and Non-Euclidean Geometries: History and Development (3rd Ed). W. H. Freeman. New York. 1994.

[G-S 1979] B. Grunbaum and G. C. Shephard. "Incidence symbols and their applications" Proceedings of Symposia in Pure Mathematics, Vol. XXXIV: Relations Between Combinatorics and Other Parts of Mathematics. American Math. Soc. Providence, RI. 1979.

[G-S 1987] B. Grunbaum and G. C. Shephard. Tilings and Patterns. W. H. Freeman. New York. 1987.

[G-S 1989] B. Grunbaum and G. C. Shephard. Tilings and Patterns: An Introduction. W. H. Freeman. New York. 1989.

[G-V] J. Gerretsen and P. Verdendium. "Polygons and theory." Fundamentals of Mathematics, Vol.II: Geometry. H. Behnke et al. (Editors). MIT Press. Cambridge, MA. 1974. Pages 265--290.

[H-CV] D.Hilbert and S. Cohn-Vossen. Geometry and the Imagination. Chelsea. New York. 1952. Pages 98--114.

[H] D. H. Huson. "The generation and classification of tile-k-transitive tilings on the Euclidean plane, sphere, and hyperbolic plane." Geometrae Dedicata, Vol. 47. 1993. Pages 295--310.

[K-F] F. Klein and R. Fricke. Theorie der Ellitischen Modulfunctionen, Vol. 1. B. G. Teubner. Leipzig. 1890. Pages 98--114.

[L] J. Lehner. A Short Course in Automorphic Functions. Holt, Rinehardt and Winston. New York. 1966.

[Mag] W. Magnus. Noneuclidean Tesselations and Their Groups. Academic Press. New York. 1974. Pages 81--85.

[Mar] G. E. Martin. Transformation Geometry: An Introduction to Symmetry. Springer-Verlag. New York. 1982. Page 199.

[P] A. Pugh. Polyhedra: A Visual Approach. Univ. of California Press. Berkeley, CA. 1976. Pages 177--182.

[R] J. F. Rigby. "Butterflies and snakes." M.C.Escher: Art and Science. H.S.M. Coxeter et al. (Editors). North-Holland. Amsterdam. 1986. Pages 211--220.

[W] T. R. S. Walsh. "Characterizing the vertex neighbourhoods of semi-regular polyhedra." Geometriae Dededicata, Vol. 1. 1972. Pages 117--123.

[We] J. Weeks. KaleidoTile. Tiling software. From Weeks' description of the program: "Use KaleidoTile to create tesselations of the sphere, Euclidean plane and hyperbolic plane. The tesselations are dynamic: the user moves a "basepoint" to smoothly transform, say, a dodecahedron into an icosahedron (or a rhombicosadodecahedron or a . . .). All tesselations may be freely rotated or translated, giving a sense of realism and fluidity."

[Z] J. Zaks. "Semi-regular polyhedra and maps." Geometriae Dededicata, Vol. 7. 1978. Pages 465--478.

Author: Kevin Mitchell (
Last Update: 13 February 1996.