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 Seymore (2001). ISBN 0-7690-2782-2. An activity-based book for classroom use.
  • Cromwell, P.; Polyhedra, Cambridge University Press, 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

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.; De harmonices Mundi (1691) (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).
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