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
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).