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

• 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

• 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 Seymore (2001). ISBN 0-7690-2782-2. An activity-based book for classroom use.
• Cromwell, P.; Polyhedra, CUP hbk (1997), pbk. (1999).
• Cundy, H.M. & Rollett, A.P.; Mathematical models, 1st Edn. hbk OUP (1951), 2nd Edn. hbk OUP (1961), 3rd Edn. pbk Tarquin (1981). ISBN 978-0-906212-20-2 Classic text.
• Holden; Shapes, space and symmetry, (1971), Dover pbk (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

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5
• Coxeter, H.S.M. DuVal, Flather & Petrie; 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.
• Richeson, D.S.; Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press (2008).
• 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.
• Stewart, B.M.; Adventures among the toroids, self-published (1970).
• Thompson, Sir D'A. W. On growth and form, (1943). (not sure if this is the right category for this one, I haven't read it).

Natural, design and architecture bias

• Critchlow, K.; Order in space, Thames & Hudson (1969).
• Pearce, P.; Structure in nature is a strategy for design, MIT (1978)
• Williams, R.; Natural structure, Eudaemon (1972). 2nd Edition renamed The geometrical foundation of natural structure, Dover (1979). 3rd Edition renamed The Geometry of Natural Structure (40th Anniversary Edition), San Francisco: Eudaemon Press (2009).ISBN 978-0-9823465-1-8
  • Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. 

Advanced mathematical texts

• Coxeter, H.S.M.; Regular Polytopes 3rd Edn. Dover (1973).
• Coxeter, H.S.M.; Regular complex polytopes, CUP (1974).
• Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
• Several more to add here.

Historic books

Listed in chronological order

• Plato; Timaeus (Greek). Includes a theory of matter based on polyhedra.
• Euclid; Elements (Greek). Construction of the five regular solids.
• Pacioli, L.; Divina proportione (1509) (Latin)
• Jamnitzer, W.; Perspectiva Corporum Regularium (1568). Woodcuts of star polyhedra and other variations.
• Kepler, J.; De harmonices Mundi (1691) (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. (German). WorldCat English: Polygons and Polyhedra: Theory and History.
• Brückner, M.; Uber die gleichecking-gleichflachigen, diskontinuierlichen und nichtkonvexen Polyheder, (1906). (German).