Steven Dutch, Professor Emeritus, Natural and Applied Sciences, Universityof 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 thisreferences 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 reallyobscure ones you may have to resort to inter-library loan.
M. J. Buerger, Elementary Crystallography, Wiley, 1956, (MIT press reprint,1978).
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-Verlag reprint, 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; thirdedition Tarquin publ., 1981. A genuine classic and one of the most likely to be in apublic library.
Peter Hilton, Jean Pedersen, Build Your Own polyhedra, Addison Wesley, 1988
Alan Holden, Shapes, Spaces and Symmetry, Columbia Univ. Pr, 1971, (Doverreprint, 1991). A delightful book full of photos of well-crafted cardboard models.
Norman W. Johnson, "Convex Solids with Regular Faces," Canadian Journal ofMathematics, 18, 1966, pp. 169-200. The complete listing of all non-regular convexsolids 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, Van Nostrand Reinhold,(reprinted by Dale Seymour Publications) 1978
Bonnie M. Stewart, Adventures Among the Toroids, 1970; 2nd ed. 1980. Privatelypublished and available from Dorris Stewart, 4494 Wausau Rd, Okemos, Michigan 48864.
Hugh Apsimon, "Three facially regular polyhedra", Canadian Journal ofMathematics, pp. 326-330, 1950.
J. R. Gott, "Pseudopolyhedrons," American Mathematical Monthly, Vol74, p. 497, 1967.
Albrecht Durer, Painter's Manual, 1525, (Abaris reprint, 1977).
Wentzel Jamnitzer, Perspectiva Corporum Regularium, Nuremberg, 1568, (GutenbergReprints, 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: Theorie und Geschichte, Teubner, 1900.
Walter William Rouse Ball, revised by H.S.M. Coxeter, Mathematical Recreations andEssays, New York, 1938; 11th ed., 1960, (Dover reprint). One of the all-time classicsin recreational mathematics.
When people see my paper models of polyhedra, they naturally wonder if I'm interestedin origami. For the most part, the answer is no, and for a somewhat surprising reasongiven the traditional image of Japanese art: most origami strikes me as not especiallyelegant. It seems trivially obvious to me that if you start with a big enough sheet ofpaper and crinkle it enough times, you can obtain any shape you like. Granted that some ofthe shapes top origami folders achieve can be pretty amazing. However modular origamidoes interest me; it's the art of creating polygons and polyhedra by paper folding. A fewreferences are below.
Tomoko Fuse, Unit Origami: Multidimensional Transformations, Japan Publications,1990.
Rona Gurkewitz, Bennet Arnstein, 3-D Geometric Origami: Modular polyhedra, Dover,1995.
Lewis Simon, Bennett Arnstein and Rona Gurkewitz, Modular Origamipolyhedra: Revised and Enlarged Edition, Dover Publications, 1999 $5.95
David Mitchell, Mathematical Origami: Geometrical Shapes by Paper Folding,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.
Subject to change without notice. Please let meknow if any links are incorrect or no longer operating.
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Created 2 March, 1999, Last Update 2 March, 1999