• Source: List of books about polyhedra

This is a list of books about polyhedra.




Polyhedral models






= Cut-out kits

=
Jenkins, Gerald; Bear, Magdalen (1998). Paper Polyhedra in Colour. Tarquin. ISBN 1-899618-23-6. Advanced Polyhedra 1: The Final Stellation, ISBN 1-899618-61-9. Advanced Polyhedra 2: The Sixth Stellation, ISBN 1-899618-62-7. Advanced Polyhedra 3: The Compound of Five Cubes, ISBN 978-1-899618-63-7.
Jenkins, Gerald; Wild, Anne (2000). Mathematical Curiosities. Tarquin. ISBN 1-899618-35-X. More Mathematical Curiosities, Tarquin, ISBN 1-899618-36-8. Make Shapes 1, ISBN 0-906212-00-6. Make Shapes 2, ISBN 0-906212-01-4.
Smith, A. G. (1986). Cut and Assemble 3-D Geometrical Shapes: 10 Models in Full Color. Dover. Cut and Assemble 3-D Star Shapes, 1997. Easy-To-Make 3D Shapes in Full Color, 2000.
Torrence, Eve (2011). Cut and Assemble Icosahedra: Twelve Models in White and Color. Dover.




= Origami

=
Fuse, Tomoko (1990). Unit Origami: Multidimensional Transformations. Japan Publications. ISBN 978-0-87040-852-6.
Gurkewitz, Rona; Arnstein, Bennett (1996). 3D Geometric Origami: Modular Origami Polyhedra. Dover. ISBN 9780486135601. Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, 2002. Beginner's Book of Modular Origami Polyhedra: The Platonic Solids, 2008. Modular Origami Polyhedra, also with Lewis Simon, 2nd ed., 1999.
Mitchell, David (1997). Mathematical Origami: Geometrical Shapes by Paper Folding. Tarquin. ISBN 978-1-899618-18-7.
Montroll, John (2009). Origami Polyhedra Design. A K Peters. ISBN 9781439871065. A Plethora of Polyhedra in Origami, Dover, 2002.




= Other model-making

=
Cundy, H. M.; Rollett, A. P. (1952). Mathematical Models. Clarendon Press. 2nd ed., 1961. 3rd ed., Tarquin, 1981, ISBN 978-0-906212-20-2.
Hilton, Peter; Pedersen, Jean (1988). Build Your Own Polyhedra. Addison-Wesley.
Wenninger, Magnus (1971). Polyhedron Models. Cambridge University Press. 2nd ed., Polyhedron Models for the Classroom, 1974. Spherical Models, 1979. Dual Models, 1983.




Mathematical studies






= Introductory level and general audience

=
Akiyama, Jin; Matsunaga, Kiyoko (2015). Treks into Intuitive Geometry: The World of Polygons and Polyhedra. Springer.
Alsina, Claudi (2017). The Thousand Faces of Geometric Beauty: The Polyhedra. Our Mathematical World. Vol. 23. National Geographic. ISBN 978-84-473-8929-2.
Britton, Jill (2001). Polyhedra Pastimes. Dale Seymour Publishing. ISBN 0-7690-2782-2.
Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press.
Fetter, Ann E. (1991). The Platonic Solids Activity Book. Key Curriculum Press.
Holden, Alan (1971). Shapes, Space and Symmetry. Dover, 1991.
le Masne, Roger (2013). Les polyèdres, ou la beauté des mathématiques (in French) (4th ed.). Self-published.
Miyazaki, Koji (1983). Katachi to kūkan: Tajigen sekai no kiseki (in Japanese). Wiley. Translated into English as An Adventure in Multidimensional Space: The Art and Geometry of Polygons, Polyhedra, and Polytopes, Wiley, 1986, and into German as Polyeder und Kosmos: Spuren einer mehrdimensionalen Welt, Vieweg, 1987.
Pearce, Peter; Pearce, Susan (1979). Polyhedra Primer. Van Nostrand Reinhold. ISBN 978-0-442-26496-3.
Pugh, Anthony (1976). Polyhedra: A Visual Approach. University of California Press.
Radin, Dan (2008). The Platonic Solids Book. Self-published.
Sutton, Daud (2002). Platonic & Archimedean Solids: The Geometry of Space. Wooden Books. ISBN 978-0802713865.




= Textbooks

=
Alexandrov, A. D. (2005). Convex Polyhedra. Springer. Translated from 1950 Russian edition.
Beck, Matthias; Robins, Sinai (2007). Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics. Vol. 154. Springer. 2nd ed., 2015, ISBN 978-1-4939-2968-9.
Brøndsted, Arne (1983). An Introduction to Convex Polytopes. Graduate Texts in Mathematics. Vol. 90. Springer.
Coxeter, H. S. M. (1948). Regular Polytopes. Methuen. 2nd ed., Macmillan, 1963. 3rd ed., Dover, 1973.
Fejes Tóth, László (1964). Regular Figures. Pergamon.
Grünbaum, Branko (1967). Convex Polytopes. Wiley. 2nd ed., Springer, 2003.
Lyusternik, Lazar (1956). Выпуклые фигуры и многогранники (in Russian). Gosudarstv. Izdat. Tehn.-Teor. Lit. Translated into English as Convex Figures and Polyhedra by T. Jefferson Smith, Dover, 1963 and by Donald L. Barnett, Heath, 1966.
Roman, Tiberiu (1968). Reguläre und halbreguläre Polyeder [Regular and semiregular polyhedra] (in German). VEB Deutscher Verlag der Wissenschaften.
Thomas, Rekha (2006). Lectures in Geometric Combinatorics. American Mathematical Society.
Ziegler, Günter M. (1993). Lectures on Polytopes. Springer.




= Monographs and special topics

=
Coxeter, H. S. M.; du Val, P.; Flather, H. T.; Petrie, J. F. (1938). The Fifty-Nine Icosahedra. University of Toronto Studies, Mathematical Series. Vol. 6. University of Toronto Press. 2nd ed., Springer, 1982. 3rd ed., Tarquin, 1999.
Coxeter, H. S. M. (1974). Regular Complex Polytopes. Cambridge University Press. 2nd ed., 1991.
Demaine, Erik; O'Rourke, Joseph (2007). Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press.
Deza, Michel; Grishukhin, Viatcheslav; Shtogrin, Mikhail (2004). Scale-Isometric Polytopal Graphs in Hypercubes and Cubic Lattices: Polytopes in Hypercubes and





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. London: Imperial College Press. doi:10.1142/9781860945489. ISBN 1-86094-421-3.
Lakatos, Imre (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press.
McMullen, Peter (2020). Geometric Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 172. Cambridge University Press.
McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 92. Cambridge University Press.
McMullen, Peter; Shephard, G. C. (1971). Convex Polytopes and the Upper Bound Conjecture. London Mathematical Society Lecture Note Series. Vol. 3. Cambridge University Press.
Nef, Walter (1978). Beiträge zur Theorie der Polyeder: Mit Anwendungen in der Computergraphik [Contributions to the theory of the polyhedron, with applications in computer graphics] (in German). Herbert Lang.
Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Vol. 21. Hindustan Book Agency.
Richter-Gebert, Jürgen (1996). Realization Spaces of Polytopes. Lecture Notes in Mathematics. Vol. 1643. Springer.
Stewart, B. M. (1970). Adventures Among the Toroids. Self-published. 2nd ed., 1980.
Wachman, Avraham; Burt, Michael; Kleinmann, M. (1974). Infinite Polyhedra. Technion. 2nd ed., 2005.
Wu, Wen-tsün (1965). A Theory of Imbedding, Immersion, and Isotopy of Polytopes in a Euclidean Space. Science Press.
Zalgaller, Viktor A. (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. Translated and corrected from Zalgaller, V. A. (1967). Выпуклые многогранники с правильными гранями. Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI) (in Russian). Vol. 2. Nauka.
Zhizhin, Gennadiy Vladimirovich (2022). The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems. Advances in Chemical and Materials Engineering. IGI Global. ISBN 9781799883760.




= Edited volumes

=
Avis, David; Bremner, David; Deza, Antoine, eds. (2009). Polyhedral Computation. CRM Proceedings and Lecture Notes. Vol. 48. American Mathematical Society.
Gabriel, Jean-François, ed. (1997). Beyond the Cube: The Architecture of Space Frames and Polyhedra. Wiley.
Kalai, Gil; Ziegler, Günter M., eds. (2012). Polytopes - Combinatorics and Computation. DMV Seminar. Vol. 29. Springer.
Senechal, Marjorie; Fleck, G., eds. (1988). Shaping Space: A Polyhedral Approach. Birkhauser. ISBN 0-8176-3351-0. 2nd ed., Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, Springer, 2013.




History






= Early works

=
Listed in chronological order, and including some works shorter than book length:

Plato. Timaeus (in Greek).
Euclid. Elements (in Greek).
Pappus of Alexandria (1589). Mathematicae collectiones, liber quintus. apud Franciscum de Franciscis Senensem.
Della Francesca, Piero (1482–1492). De quinque corporibus regularibus [On the five regular bodies] (in Latin).
Pacioli, Luca (1509). Divina proportione [Divine proportion] (in Italian).
de Bovelles, Charles (1511). De mathematicis corporibus.
Dürer, Albrecht (1525). Underweysung der Messung, mit dem Zirckel und Richtscheyt, in Linien, Ebenen und gantzen corporen, Viertes Buch (in German).
Maurolico, Francesco (1537). Compaginationes solidorum regularium.
Jamnitzer, Wenzel (1568). Perspectiva corporum regularium [Perspectives of the regular bodies].
Kepler, Johannes (1619). Harmonices Mundi (in Latin). Translated into English as Harmonies of the World by C. G. Wallis (1939).
Descartes, René (c. 1630). De solidorum elementis [On the elements of solids] (in Latin). Original manuscript lost; copy by Gottfried Wilhelm Leibniz reprinted and translated in Descartes on Polyhedra, Springer, 1982.
Cowley, John Lodge (1758). An Appendix to Euclid's Elements in Seven Books, Containing Forty-two Copper-plates, In Which the Doctrine of Solids, Delivered in the XIth, XIIth, and XVth Books of Euclid, is Illustrated by New-invented Schemes Cut Out of Paste-Board. Watkins.
Poinsot, Louis (1810). Mémoire sur les polygones et sur les polyèdres (in French).
Marie, François-Charles-Michel (1835). Géométrie stéréographique, ou reliefs des polyèdres (in French). Paris. hdl:2027/ucm.531073766x.
Schläfli, Ludwig (1901) [1852]. Graf, J. H. (ed.). Theorie der vielfachen Kontinuität. Republished by Cornell University Library historical math monographs 2010 (in German). Zürich, Basel: Georg & Co. ISBN 978-1-4297-0481-6.
Wiener, Christian (1864). Über Vielecke und Vielflache. Teubner.
Catalan, Eugène (1865). "Mémoire sur la théorie des polyèdres". Journal de l'École Polytechnique (in French). 24. hdl:2268/194785.
Klein, Felix (1884). Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5ten Grade [Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree] (in German).
Fedorov, E. S. (1885). Начала учения о фигурах [Introduction to the Theory of Figures] (in Russian).
Gorham, John (1888). A System for the Construction of Crystal Models on the Type of an Ordinary Plait: Exemplified by the Forms Belonging to the Six Axial Systems in Crystallography. Reprint, Tarquin, 2007, ISBN 978-1-899618-68-2.
Eberhard, Victor (1891). Zur Morphologie der Polyeder [On the morphology of polyhedra]. Teubner.
von Lindemann, Ferdinand (1897). Zur Geschichte der Polyeder und der Zahlzeichen [History of Polyhedra and Numeral Signs] (in German). Munich: F. Straub. Reprinted from Sitz. Bay. Akad. Wiss. 1896, pp. 625–758.
Brückner, Max (1900). Vielecke und Vielflache: Theorie und Geschichte (in German). Treubner. Über die gleicheckig-gleichflächigen diskontinuierlichen und nichtkonvexen Polyeder, 1906.
Steinitz, Ernst (1934). Rademacher, Hans (ed.). Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie (in German).




= Books about historical topics

=
Andrews, Noam (2022). The Polyhedrists: Art and Geometry in the Long Sixteenth Century. MIT Press.
Davis, Margaret Daly (1977). Piero della Francesca's Mathematical Treatises: The "Trattato d'abaco" and "Libellus de quinque corporibus regularibus". Longo.
Dézarnaud-Dandine, Christine; Sevin, Alain (2009). Histoire des polyèdres: Quand la nature est géomètre (in French). Vuibert.
Federico, Pasquale Joseph (1984). Descartes on Polyhedra: A Study of the "De solidorum elementis". Sources in the History of Mathematics and Physical Sciences. Vol. 4. Springer.
Richeson, D. S. (2008). Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press.
Sanders, Philip Morris (1990). The Regular Polyhedra in Renaissance Science and Philosophy. Warburg Institute, University of London.
Wade, David (2012). Fantastic Geometry: Polyhedra and the Artistic Imagination in the Renaissance. Squeeze Press.




References

Kata Kunci Pencarian:

• Bangun ruang Platonik
• Daftar masalah matematika yang belum terpecahkan
• List of books about polyhedra
• Polyhedron
• Polyhedra (book)
• Convex Polyhedra (book)
• List of books in computational geometry
• Descartes on Polyhedra
• Platonic solid
• Euler's Gem
• Regular Polytopes (book)
• Adventures Among the Toroids