List of books about polyhedra

This is a list of books about polyhedra.

Books of cut-out kits for making card models

• Jenkins, G. and Bear, M.; Advanced Polyhedra 1: The Final Stellation, Tarquin. ISBN 1-899618-61-9
• Jenkins, G. and Bear, M.; Advanced Polyhedra 2: The Sixth Stellation, Tarquin. ISBN 1-899618-62-7
• Jenkins, G. and Bear, M.; Advanced Polyhedra 3: The Compound of Five Cubes, Tarquin. ISBN 978-1-899618-63-7
• Jenkins, G. and Wild, A.; Mathematical Curiosities, Tarquin. ISBN 1-899618-35-X
• Jenkins, G. and Wild, A.; More Mathematical Curiosities, Tarquin. ISBN 1-899618-36-8
• Jenkins, G. and Wild, A.; Make shapes 1, various editions, Tarquin. Simple convex and star polyhedra ISBN 0-906212-00-6
• Jenkins, G. and Wild, A.; Make shapes 2, various editions, Tarquin. Convex and star polyhedra ISBN 0-906212-01-4
• Jenkins, G. and Bear, M.; Paper Polyhedra in Colour, Tarquin. ISBN 1-899618-23-6
• Smith, A.G.; Cut and assemble 3-D geometrical shapes: 10 models in full color, Dover (1986). Convex and star polyhedra.
• Smith, A.G.; Cut and assemble 3-D star shapes, Dover (1997). Star polyhedra.
• Smith, A.G.; Easy-to-make 3D shapes in full color, Dover (2000). Simple convex polyhedra.

Instructions for making models

• Fuse, T.; Unit Origami: Multidimensional Transformations, Japan Publications (1990). ISBN 0-87040-852-6, ISBN 978-0-87040-852-6. Contains origami instructions to build many polyhedra. The shapes vary from simple to extremely complex. The book focuses on origami and construction.
• Gorham, J.; Crystal models: on the type of an ordinary plait (1888). Reprint, Ed. Sharp, J., Tarquin (2007), also includes reprinted articles by Pargeter, R. and Brunton, J. ISBN 978-1-899618-68-2
• Gurkewitz, R, Arnstein, B; "3D Geometric Origami: Modular Origami Polyhedra", Dover Publications (1996)
• Hilton, P., Carlisle, P., Lewis, M. & Pedersen, J,; Build Your Own Polyhedra, Dale Seymour; 2nd edition (1994). ISBN 0-201-49096-X, ISBN 978-0-201-49096-1. Contains instructions for building the Platonic solids and other shapes using paper tape. The focus audience is teachers. Includes some mathematics.
• Mitchell, D.; Mathematical origami: geometrical shapes and paper folding, Tarquin (1997). ISBN 978-1-899618-18-7
• Montroll, John; Origami Polyhedra Design, A K Peters, 2009
• Wenninger, M.; Polyhedron models for the classroom, pbk (1974)
• Wenninger, M.; Polyhedron models, CUP hbk (1971), pbk (1974). Classic work giving instructions for all the uniform polyhedra and some stellations. Includes some basic theory.
• Wenninger, M.; Spherical models, CUP. Includes some basic theory.
• Wenninger, M.; Dual models, CUP hbk (1983), pbk (2003). Instructions for all the uniform dual polyhedra. Includes some theoretical discussion.

Introductory books, also suitable for school use

• Britton, J., Polyhedra Pastimes, Dale Seymour Publishing, 2001, ISBN 0-7690-2782-2.
• Cromwell, P., Polyhedra, Cambridge University Press, 1997.
• Cundy, H. M. and Rollett, A. P., Mathematical models, Oxford University Press, 1951; 3rd ed., Tarquin, 1981, ISBN 978-0-906212-20-2.
• Holden, A., Shapes, space and symmetry, 1971; Dover, 1991.
• Pearce, P. and Pearce, S., Polyhedra primer, Van Nost. Reinhold, 1979, ISBN 0-442-26496-8, ISBN 978-0-442-26496-3.
• Ball, W. W. R. and Coxeter, H. S. M., Mathematical recreations and essays, Dover, 13th Edn (1987). Editions up to the 10th were written by Ball. Chapter V provides an introduction to polyhedra.
• Wachman, A., Burt, M. and Kleinmann, M.; Infinite polyhedra, Technion, 1st Edn. (1974), 2nd Edn. (2005). Pictorial and photographic representations.

Undergraduate level

• Beck, Matthias and Robins, Sinai; Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra, Springer, Undergraduate Texts in Mathematics, 2nd ed., 2015, ISBN 978-1-4939-2968-9
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
• Coxeter, H.S.M., DuVal, P., Flather, H. T., and Petrie, J. F.; The fifty-nine icosahedra, 3rd Edn. Tarquin.
• Coxeter, H.S.M.; Twelve geometric essays (1968). Republished as The beauty of geometry: Twelve essays, Dover (1999). Almost half the essays discuss polyhedra or related topics.
• Fejes Tóth, L.; Regular figures, Pergamon (1964).
• Lakatos, I.; Proofs and Refutations, Cambridge University Press, 1976 – Discussion of proofs of the Euler characteristic.
• Hilton, P. and Pedersen, J.; A mathematical tapestry: demonstrating the beautiful unity of mathematics, Cambridge University Press (2010). ISBN 0-521-12821-8. About half the chapters discuss polyhedra and their relationships to other areas of mathematics.
• Senechal, M. & Fleck, G. (Eds); Shaping Space: A Polyhedral Approach, Birkhauser (1988), ISBN 0-8176-3351-0. Based on workshops and papers presented at the Shaping Space Conference, Smith College, April 1984. Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, 2nd ed., Springer, 2013.
• Stewart, B.M.; Adventures Among the Toroids, self-published (1970; 2nd ed., 1980).
• Thompson, Sir D'A. W.; On growth and form (1943).

Advanced mathematical texts

• Alexandrov, A. D., Convex Polyhedra, Springer, 2005 (translated from 1950 Russian edition)
• Coxeter, H.S.M., Regular Polytopes 3rd ed. Dover, 1973.
• Coxeter, H.S.M., Regular complex polytopes, Cambridge University Press, 1974.
• Coxeter, H.S.M., Kaleidoscopes: Selected Writings, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
• Grünbaum, Branko, Convex Polytopes, Springer, 1967, 2nd ed. 2003
• McMullen, Peter & Schulte, Egon, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications 92, Cambridge University Press, 2002
• McMullen, Peter, Geometric Regular Polytopes, Encyclopedia of Mathematics and its Applications 172, Cambridge University Press, 2020
• Richter-Gebert, Jürgen, Realization Spaces of Polytopes, Springer, 1996
• Thomas, Rekha, Lectures in Geometric Combinatorics, Amer. Math. Soc. 2006
• Ziegler, Günter M., Lectures on Polytopes, Springer, 1993

Historic books

Listed in chronological order.

• Plato; Timaeus (in Greek). Includes a theory of matter based on polyhedra.
• Euclid; Elements (in Greek). Construction of the five regular solids.
• Pacioli, L.; Divina proportione (1509) (in Latin)
• Jamnitzer, W.; Perspectiva Corporum Regularium (1568). Woodcuts of star polyhedra and other variations.
• Kepler, J.; Harmonices Mundi (1619) (in Latin). English translation: Harmonies of the World, translated by Wallis, C.G. (1939), reprinted Forgotten (2008)
• Brückner, M.; Vielecke und Vielflache: Theorie und Geschichte, Treubner (1900). ISBN 978-1-4181-6590-1. (in German). WorldCat English: Polygons and Polyhedra: Theory and History.
• Brückner, M.; Über die gleicheckig-gleichflächigen diskontinuierlichen und nichtkonvexen Polyeder (1906). (in German).

Books on the history of polyhedra

• Pasquale Joseph Federico, Descartes on Polyhedra: A Study of the "De solidorum elementis", Sources in the History of Mathematics and Physical Sciences 4, Springer, 1984
• Richeson, D. S.; Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press (2008).