List of books about polyhedra

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This is a list of books about polyhedra.

Books of cut-out kits for making card models[edit]

  • 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[edit]

  • 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
  • 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[edit]

  • 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[edit]

  • 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).

Natural, design and architecture bias[edit]

  • 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

Advanced mathematical texts[edit]

Historic books[edit]

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).