References and Links on polyhedra and Symmetry

Steven Dutch, Professor Emeritus, Natural and Applied Sciences,University of Wisconsin - Green Bay


This is not meant to be exhaustive, but since these pages get a fair number of hits, and a lot of visitors are simply looking for a place to get started, I have created this references and links page. Public libraries may have some of the more elementary works, but you're more likely to find these sources at a university library. For some really obscure ones you may have to resort to inter-library loan.

Symmetry and Crystallography

M. J. Buerger, Elementary Crystallography, Wiley,1956, (MIT press reprint, 1978).

General Works on polyhedra

H.S.M. Coxeter, M.S. Longuet-Higgins, and J.C.P. Miller, "Uniform polyhedra,"Philosophical Transactions of the Royal Society, Ser. A, 246, pp.401-449, 1953.

H.S.M. Coxeter, P. DuVal, H.T. Flather, and J.F. Petrie,The Fifty-Nine Icosahedra, U. Toronto Pr., 1938, (Springer-Verlagreprint, 1982).

K. Critchlow, Order in Space: a design source book,Viking, 1970.

Peter R. Cromwell, polyhedra, Cambridge, 1997.

H. Martyn Cundy and A.P. Rollett, Mathematical Models,Oxford, 1961; third edition Tarquin publ., 1981. A genuine classic and one of the most likely to be in a public library.

Peter Hilton, Jean Pedersen, Build Your Own polyhedra,Addison Wesley, 1988

Alan Holden, Shapes, Spaces and Symmetry, ColumbiaUniv. Pr, 1971, (Dover reprint, 1991). A delightful book full of photos of well-crafted cardboard models.

Norman W. Johnson, "Convex Solids with Regular Faces,"Canadian Journal of Mathematics, 18, 1966, pp. 169-200. The complete listing of all non-regular convex solids with regular polygon faces.

J. Skilling, "The Complete Set of Uniform polyhedra," PhilosophicalTransactions of the Royal Society, Ser. A, 278, pp. 111-135, 1975.

Peter Pearce and Susan Pearce, polyhedra Primer, VanNostrand Reinhold, (reprinted by Dale Seymour Publications) 1978

Bonnie M. Stewart, Adventures Among the Toroids, 1970; 2nd ed. 1980. Privately published and available from Dorris Stewart, 4494 Wausau Rd, Okemos, Michigan 48864.

Infinite or "Hyperbolic" Tesselations

Hugh Apsimon, "Three facially regular polyhedra", Canadian Journalof Mathematics, pp. 326-330, 1950.

J. R. Gott, "Pseudopolyhedrons," American MathematicalMonthly, Vol 74, p. 497, 1967.

Historical Classics

Albrecht Durer, Painter's Manual, 1525, (Abarisreprint, 1977).

Wentzel Jamnitzer, Perspectiva Corporum Regularium,Nuremberg, 1568, (Gutenberg Reprints, Paris 1981). Earliest extant drawings of a number of polyhedra.

Johannes Kepler, The Harmony of the World, 1625,(transl. E.J. Aiton, A.M. Duncan, and J.V. Field, 1997, American Philosophical Society).

Max Brueckner, Vielecke und Vielflache: Theorieund Geschichte, Teubner, 1900.

Walter William Rouse Ball, revised by H.S.M. Coxeter, MathematicalRecreations and Essays, New York, 1938; 11th ed., 1960, (Dover reprint). One of the all-time classics in recreational mathematics.


When people see my paper models of polyhedra, they naturally wonder if I'm interested in origami. For the most part, the answer is no, and for a somewhat surprising reason given the traditional image of Japanese art: most origami strikes me as not especially elegant. It seems trivially obvious to me that if you start with a big enough sheet of paper and crinkle it enough times, you can obtain any shape you like. Granted that some of the shapes top origami folders achieve can be pretty amazing. However modular origami does interest me; it's the art of creating polygons and polyhedra by paper folding. A few references are below.

Tomoko Fuse, Unit Origami: Multidimensional Transformations,Japan Publications, 1990.

Rona Gurkewitz, Bennet Arnstein, 3-D Geometric Origami:Modular polyhedra, Dover, 1995.

David Mitchell, Mathematical Origami: Geometrical Shapes by PaperFolding, Tarquin Publ., 1997.

Lewis Simon and Bennett Arnstein, Modular Origami polyhedra,Bennett Arnstein, 1989 (ISBN 0-9620058-1-9).

Makoto Yamaguchi, Kusudama: Ball Origami, Shufunotomo,Tokyo, 1990.

Steven I. Dutch

, "Folding n-pointed Stars and Snowflakes", The Mathematics Teacher, v. 87, no. 8, p. 630-637 (November, 1994). Not exactly origami, but related.

Links to Other Sites

Subject to change without notice. Please let me know if any links are incorrect or no longer operating.

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Created 2 March, 1999, Last Update 2 March, 1999