Polyhedron (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Polyhedron" in English language version.

refsWebsite

Global rank English rank

58doi.org

2^nd place

42ams.org

451^st place

277^th place

14books.google.com

3^rd place

14semanticscholar.org

11^th place

8^th place

9jstor.org

26^th place

20^th place

5harvard.edu

18^th place

17^th place

4psu.edu

207^th place

136^th place

3worldcat.org

5^th place

3washington.edu

1,067^th place

749^th place

2encyclopediaofmath.org

3,863^rd place

2,637^th place

2web.archive.org

1^st place

2arxiv.org

69^th place

59^th place

2handle.net

102^nd place

76^th place

1gbv.de

low place

1wias-berlin.de

low place

1projecteuclid.org

3,707^th place

2,409^th place

1bridgesmathart.org

low place

1eudml.org

low place

ams.org

mathscinet.ams.org

Lakatos, Imre (2015) [1976], Worrall, John; Zahar, Elie (eds.), Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press, p. 16, doi:10.1017/CBO9781316286425, ISBN 978-1-107-53405-6, MR 3469698, definitions are frequently proposed and argued about.
Grünbaum, Branko (1994), "Polyhedra with hollow faces", in Bisztriczky, Tibor; McMullen, Peter; Schneider, Rolf; Weiss, A. (eds.), Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational, Dordrecht: Kluwer Acad. Publ., pp. 43–70, doi:10.1007/978-94-011-0924-6_3, ISBN 978-94-010-4398-4, MR 1322057; for quote, see p. 43.
Cromwell, Peter R. (1997), Polyhedra, Cambridge: Cambridge University Press, ISBN 978-0-521-55432-9, MR 1458063; for definitions of polyhedra, see pp. 206–209; for polyhedra with equal regular faces, see p. 86.
Grünbaum, Branko (1999), "Acoptic polyhedra" (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 2021-08-30, retrieved 2022-07-01.
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027, MR 1756651.
Burgiel, H.; Stanton, D. (2000), "Realizations of regular abstract polyhedra of types {3,6} and {6,3}", Discrete and Computational Geometry, 24 (2–3): 241–255, doi:10.1007/s004540010030, MR 1758047.
Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics, vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487
Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), New York: Springer-Verlag, p. 26, doi:10.1007/978-1-4613-0019-9, ISBN 978-0-387-00424-2, MR 1976856.
Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Grünbaum, Branko (2009), "An enduring error" (PDF), Elemente der Mathematik, 64 (3): 89–101, doi:10.4171/EM/120, MR 2520469. Reprinted in Pitici, Mircea, ed. (2011), The Best Writing on Mathematics 2010, Princeton University Press, pp. 18–31.
Berman, Martin (1971), "Regular-faced convex polyhedra", Journal of the Franklin Institute, 291 (5): 329–352, doi:10.1016/0016-0032(71)90071-8, MR 0290245.
Richeson, David S. (2008), Euler's Gem: The polyhedron formula and the birth of topology, Princeton, NJ: Princeton University Press, ISBN 978-0-691-12677-7, MR 2440945, pp. 157, 180.
Cundy, H. Martyn; Rollett, A.P. (1961), "3.2 Duality", Mathematical models (2nd ed.), Oxford: Clarendon Press, pp. 78–79, MR 0124167.
Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.
Barnette, David (1973), "A proof of the lower bound conjecture for convex polytopes", Pacific Journal of Mathematics, 46 (2): 349–354, doi:10.2140/pjm.1973.46.349, MR 0328773
Hartshorne, Robin (2000), "Example 44.2.3, the "punched-in icosahedron"", Geometry: Euclid and beyond, Undergraduate Texts in Mathematics, Springer-Verlag, New York, p. 442, doi:10.1007/978-0-387-22676-7, ISBN 0-387-98650-2, MR 1761093
Sydler, J.-P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (in French), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371
Debrunner, Hans E. (1980), "Über Zerlegungsgleichheit von Pflasterpolyedern mit Würfeln", Archiv der Mathematik (in German), 35 (6): 583–587, doi:10.1007/BF01235384, MR 0604258, S2CID 121301319.
Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry, 99 (1–2): 1–13, arXiv:0901.2989, CiteSeerX 10.1.1.243.7674, doi:10.1007/s00022-011-0061-7, MR 2823098, S2CID 17515249.
Taylor, Jean E. (1992), "Zonohedra and generalized zonohedra", American Mathematical Monthly, 99 (2): 108–111, doi:10.2307/2324178, JSTOR 2324178, MR 1144350.
Demaine, Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge, pp. 345–348, doi:10.1017/CBO9780511735172, ISBN 978-0-521-85757-4, MR 2354878.
O'Rourke, Joseph (2008), "Unfolding orthogonal polyhedra", Surveys on discrete and computational geometry, Contemp. Math., vol. 453, Amer. Math. Soc., Providence, RI, pp. 307–317, doi:10.1090/conm/453/08805, ISBN 978-0-8218-4239-3, MR 2405687.
Coxeter, H.S.M. (1974), Regular Complex Polytopes, Cambridge: Cambridge University Press, MR 0370328. ^{[page needed]}
Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Knorr, Wilbur (1983), "On the transmission of geometry from Greek into Arabic", Historia Mathematica, 10 (1): 71–78, doi:10.1016/0315-0860(83)90034-4, MR 0698139
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Montebelli, Vico (2015), "Luca Pacioli and perspective (part I)", Lettera Matematica, 3 (3): 135–141, doi:10.1007/s40329-015-0090-4, MR 3402538, S2CID 193533200
Ghomi, Mohammad (2018), "Dürer's unfolding problem for convex polyhedra" (PDF), Notices of the American Mathematical Society, 65 (1): 25–27, doi:10.1090/noti1609, MR 3726673
Field, J. V. (1979), "Kepler's star polyhedra", Vistas in Astronomy, 23 (2): 109–141, Bibcode:1979VA.....23..109F, doi:10.1016/0083-6656(79)90001-1, MR 0546797
Federico, Pasquale Joseph (1982), Descartes on Polyhedra: A Study of the "De solidorum elementis", Sources in the History of Mathematics and Physical Sciences, vol. 4, Springer-Verlag, ISBN 0-387-90760-2, MR 0680214
Francese, Christopher; Richeson, David (2007), "The flaw in Euler's proof of his polyhedral formula", The American Mathematical Monthly, 114 (4): 286–296, doi:10.1080/00029890.2007.11920417, MR 2281926, S2CID 10023787
Alexanderson, Gerald L. (2006), "About the cover: Euler and Königsberg's bridges: a historical view", American Mathematical Society, New Series, 43 (4): 567–573, doi:10.1090/S0273-0979-06-01130-X, MR 2247921
Eckmann, Beno (2006), "The Euler characteristic – a few highlights in its long history", Mathematical Survey Lectures 1943–2004, Springer, pp. 177–188, doi:10.1007/978-3-540-33791-1_15, ISBN 978-3-540-33791-1, MR 2269092
Grünbaum, Branko (1994), "Regular polyhedra", in Grattan-Guinness, I. (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, vol. 2, Routledge, pp. 866–876, ISBN 0-415-03785-9, MR 1469978
Grünbaum, Branko (2007), "Graphs of polyhedra; polyhedra as graphs", Discrete Mathematics, 307 (3–5): 445–463, doi:10.1016/j.disc.2005.09.037, hdl:1773/2276, MR 2287486
Coxeter, H.S.M.; Du Val, P.; Flather, H.T.; Petrie, J.F. (1999) [1938], The Fifty-Nine Icosahedra, Tarquin Publications, ISBN 978-1-899618-32-3, MR 0676126.
Mitchell, Joseph S. B.; Mount, David M.; Papadimitriou, Christos H. (1987), "The discrete geodesic problem", SIAM Journal on Computing, 16 (4): 647–668, doi:10.1137/0216045, MR 0899694

ams.org

Timofeenko, A. V. (2010), "Junction of Non-composite Polyhedra" (PDF), St. Petersburg Mathematical Journal, 21 (3): 483–512, doi:10.1090/S1061-0022-10-01105-2.
Ghomi, Mohammad (2018), "Dürer's unfolding problem for convex polyhedra" (PDF), Notices of the American Mathematical Society, 65 (1): 25–27, doi:10.1090/noti1609, MR 3726673
Malkevitch, Joseph (2018), "Regular-faced polyhedra: remembering Norman Johnson", AMS Feature column, American Mathematical Society, retrieved 2023-05-27
Austin, David (November 2013), "Fedorov's five parallelohedra", AMS Feature Column, American Mathematical Society

arxiv.org

Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry, 99 (1–2): 1–13, arXiv:0901.2989, CiteSeerX 10.1.1.243.7674, doi:10.1007/s00022-011-0061-7, MR 2823098, S2CID 17515249.
Sparavigna, Amelia Carolina (2012), An Etruscan dodecahedron, arXiv:1205.0706

books.google.com

Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Kern, William F.; Bland, James R. (1938), Solid Mensuration with proofs, p. 75.
Diudea, M. V. (2018), Multi-shell Polyhedral Clusters, Springer, p. 39, doi:10.1007/978-3-319-64123-2, ISBN 978-3-319-64123-2.
Hartshorne (2000), p. 464.
Peirce, Charles S. (1976), Eisele, Carolyn (ed.), The New Elements of Mathematics, Volume II: Algebra and Geometry, Mouton Publishers & Humanities Press, p. 297, ISBN 9783110818840
O'Keefe, Michael; Hyde, Bruce G. (2020) [1996], Crystal Structures: Patterns and Symmetry, Dover Publications, p. 134, ISBN 9780486836546
Coxeter, H. S. M. (1947), Regular Polytopes, Methuen, p. 16
Popko, Edward S. (2012), Divided Spheres: Geodesics and the Orderly Subdivision of the Sphere, CRC Press, p. 463, ISBN 978-1-4665-0430-1, A hosohedron is only possible on a sphere.
Kraynik, A.M.; Reinelt, D.A. (2007), "Foams, Microrheology of", in Mortensen, Andreas (ed.), Concise Encyclopedia of Composite Materials (2nd ed.), Elsevier, pp. 402–407. See in particular p. 403: "foams consist of polyhedral gas bubbles ... each face on a polyhedron is a minimal surface with uniform mean curvature ... no face can be a flat polygon with straight edges".
Pearce, P. (1978), "14 Saddle polyhedra and continuous surfaces as environmental structures", Structure in nature is a strategy for design, MIT Press, p. 224, ISBN 978-0-262-66045-7.
Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419
Rashed, Roshdi (2009), "Thābit ibn Qurra et l'art de la mesure", in Rashed, Roshdi (ed.), Thābit ibn Qurra: Science and Philosophy in Ninth-Century Baghdad, Scientia Graeco-Arabica (in French), vol. 4, Walter de Gruyter, pp. 173–175, ISBN 9783110220780
Saffaro, Lucio (1992), "Cosmoids, fullerenes and continuous polygons", in Taliani, C.; Ruani, G.; Zamboni, R. (eds.), Fullerenes: Status and Perspectives, Proceedings of the 1st Italian Workshop, Bologna, Italy, 6–7 February, Singapore: World Scientific, pp. 55–64
Grünbaum, Branko (1994), "Regular polyhedra", in Grattan-Guinness, I. (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, vol. 2, Routledge, pp. 866–876, ISBN 0-415-03785-9, MR 1469978

bridgesmathart.org

archive.bridgesmathart.org

Luotoniemi, Taneli (2017), "Crooked houses: Visualizing the polychora with hyperbolic patchwork", in Swart, David; Séquin, Carlo H.; Fenyvesi, Kristóf (eds.), Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, Phoenix, Arizona: Tessellations Publishing, pp. 17–24, ISBN 978-1-938664-22-9

doi.org

Lakatos, Imre (2015) [1976], Worrall, John; Zahar, Elie (eds.), Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press, p. 16, doi:10.1017/CBO9781316286425, ISBN 978-1-107-53405-6, MR 3469698, definitions are frequently proposed and argued about.
Grünbaum, Branko (1994), "Polyhedra with hollow faces", in Bisztriczky, Tibor; McMullen, Peter; Schneider, Rolf; Weiss, A. (eds.), Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational, Dordrecht: Kluwer Acad. Publ., pp. 43–70, doi:10.1007/978-94-011-0924-6_3, ISBN 978-94-010-4398-4, MR 1322057; for quote, see p. 43.
Loeb, Arthur L. (2013), "Polyhedra: Surfaces or solids?", in Senechal, Marjorie (ed.), Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination (2nd ed.), Springer, pp. 65–75, doi:10.1007/978-0-387-92714-5_5, ISBN 978-0-387-92713-8
O'Rourke, Joseph (1993), "Computational Geometry in C" (PDF), Computers in Physics, 9 (1): 113–116, Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371.
Grünbaum, Branko (1999), "Acoptic polyhedra" (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 2021-08-30, retrieved 2022-07-01.
Bokowski, J.; Guedes de Oliveira, A. (2000), "On the generation of oriented matroids", Discrete and Computational Geometry, 24 (2–3): 197–208, doi:10.1007/s004540010027, MR 1756651.
Burgiel, H.; Stanton, D. (2000), "Realizations of regular abstract polyhedra of types {3,6} and {6,3}", Discrete and Computational Geometry, 24 (2–3): 241–255, doi:10.1007/s004540010030, MR 1758047.
Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics, vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487
Grünbaum, Branko (2003), Convex Polytopes, Graduate Texts in Mathematics, vol. 221 (2nd ed.), New York: Springer-Verlag, p. 26, doi:10.1007/978-1-4613-0019-9, ISBN 978-0-387-00424-2, MR 1976856.
Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Boissonnat, J. D.; Yvinec, M. (June 1989), Probing a scene of non convex polyhedra, Proceedings of the fifth annual symposium on Computational geometry, pp. 237–246, doi:10.1145/73833.73860.
Grünbaum, Branko (2009), "An enduring error" (PDF), Elemente der Mathematik, 64 (3): 89–101, doi:10.4171/EM/120, MR 2520469. Reprinted in Pitici, Mircea, ed. (2011), The Best Writing on Mathematics 2010, Princeton University Press, pp. 18–31.
Diudea, M. V. (2018), Multi-shell Polyhedral Clusters, Springer, p. 39, doi:10.1007/978-3-319-64123-2, ISBN 978-3-319-64123-2.
Cundy, H. Martyn (1952), "Deltahedra", Mathematical Gazette, 36: 263–266, doi:10.2307/3608204, JSTOR 3608204.
Berman, Martin (1971), "Regular-faced convex polyhedra", Journal of the Franklin Institute, 291 (5): 329–352, doi:10.1016/0016-0032(71)90071-8, MR 0290245.
Timofeenko, A. V. (2010), "Junction of Non-composite Polyhedra" (PDF), St. Petersburg Mathematical Journal, 21 (3): 483–512, doi:10.1090/S1061-0022-10-01105-2.
Schramm, Oded (1992-12-01), "How to cage an egg", Inventiones Mathematicae, 107 (1): 543–560, Bibcode:1992InMat.107..543S, doi:10.1007/BF01231901, ISSN 1432-1297.
Bridge, N.J. (1974), "Facetting the dodecahedron", Acta Crystallographica, A30 (4): 548–552, Bibcode:1974AcCrA..30..548B, doi:10.1107/S0567739474001306.
Inchbald, G. (2006), "Facetting diagrams", The Mathematical Gazette, 90 (518): 253–261, doi:10.1017/S0025557200179653, S2CID 233358800.
Ringel, Gerhard (1974), "Classification of surfaces", Map Color Theorem, Springer, pp. 34–53, doi:10.1007/978-3-642-65759-7_3, ISBN 978-3-642-65761-0
Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.
Barnette, David (1973), "A proof of the lower bound conjecture for convex polytopes", Pacific Journal of Mathematics, 46 (2): 349–354, doi:10.2140/pjm.1973.46.349, MR 0328773
Coxeter, H. S. M. (January 1930), "The polytopes with regular-prismatic vertex figures", Philosophical Transactions of the Royal Society of London, Series A, 229 (670–680), The Royal Society: 329–425, Bibcode:1930RSPTA.229..329C, doi:10.1098/rsta.1930.0009
Hartshorne, Robin (2000), "Example 44.2.3, the "punched-in icosahedron"", Geometry: Euclid and beyond, Undergraduate Texts in Mathematics, Springer-Verlag, New York, p. 442, doi:10.1007/978-0-387-22676-7, ISBN 0-387-98650-2, MR 1761093
Büeler, B.; Enge, A.; Fukuda, K. (2000), "Exact Volume Computation for Polytopes: A Practical Study", Polytopes — Combinatorics and Computation, pp. 131–154, CiteSeerX 10.1.1.39.7700, doi:10.1007/978-3-0348-8438-9_6, ISBN 978-3-7643-6351-2
Sydler, J.-P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (in French), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371
Debrunner, Hans E. (1980), "Über Zerlegungsgleichheit von Pflasterpolyedern mit Würfeln", Archiv der Mathematik (in German), 35 (6): 583–587, doi:10.1007/BF01235384, MR 0604258, S2CID 121301319.
Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry, 99 (1–2): 1–13, arXiv:0901.2989, CiteSeerX 10.1.1.243.7674, doi:10.1007/s00022-011-0061-7, MR 2823098, S2CID 17515249.
Taylor, Jean E. (1992), "Zonohedra and generalized zonohedra", American Mathematical Monthly, 99 (2): 108–111, doi:10.2307/2324178, JSTOR 2324178, MR 1144350.
Demaine, Erik D.; O'Rourke, Joseph (2007), "23.2 Flexible polyhedra", Geometric Folding Algorithms: Linkages, origami, polyhedra, Cambridge University Press, Cambridge, pp. 345–348, doi:10.1017/CBO9780511735172, ISBN 978-0-521-85757-4, MR 2354878.
O'Rourke, Joseph (2008), "Unfolding orthogonal polyhedra", Surveys on discrete and computational geometry, Contemp. Math., vol. 453, Amer. Math. Soc., Providence, RI, pp. 307–317, doi:10.1090/conm/453/08805, ISBN 978-0-8218-4239-3, MR 2405687.
Gardner, Martin (November 1966), "Mathematical Games: Is it possible to visualize a four-dimensional figure?", Scientific American, 215 (5): 138–143, doi:10.1038/scientificamerican1166-138, JSTOR 24931332
Coxeter, H.S.M. (1985), "A special book review: M.C. Escher: His life and complete graphic work", The Mathematical Intelligencer, 7 (1): 59–69, doi:10.1007/BF03023010, S2CID 189887063 Coxeter's analysis of Stars is on pp. 61–62.
Grötschel, Martin; Lovász, László; Schrijver, Alexander (1993), Geometric algorithms and combinatorial optimization, Algorithms and Combinatorics, vol. 2 (2nd ed.), Springer-Verlag, Berlin, doi:10.1007/978-3-642-78240-4, ISBN 978-3-642-78242-8, MR 1261419
Kitchen, K. A. (October 1991), "The chronology of ancient Egypt", World Archaeology, 23 (2): 201–208, doi:10.1080/00438243.1991.9980172
Gunn, Battiscombe; Peet, T. Eric (May 1929), "Four Geometrical Problems from the Moscow Mathematical Papyrus", The Journal of Egyptian Archaeology, 15 (1): 167–185, doi:10.1177/030751332901500130, S2CID 192278129
Eves, Howard (January 1969), "A geometry capsule concerning the five platonic solids", Historically Speaking, The Mathematics Teacher, 62 (1): 42–44, doi:10.5951/mt.62.1.0042, JSTOR 27958041
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Bréard, Andrea; Cook, Constance A. (December 2019), "Cracking bones and numbers: solving the enigma of numerical sequences on ancient Chinese artifacts", Archive for History of Exact Sciences, 74 (4): 313–343, doi:10.1007/s00407-019-00245-9, S2CID 253898304
van der Waerden, B. L. (1983), "Chapter 7: Liu Hui and Aryabhata", Geometry and Algebra in Ancient Civilizations, Springer, pp. 192–217, doi:10.1007/978-3-642-61779-9_7
Knorr, Wilbur (1983), "On the transmission of geometry from Greek into Arabic", Historia Mathematica, 10 (1): 71–78, doi:10.1016/0315-0860(83)90034-4, MR 0698139
Hisarligil, Hakan; Hisarligil, Beyhan Bolak (December 2017), "The geometry of cuboctahedra in medieval art in Anatolia", Nexus Network Journal, 20 (1): 125–152, doi:10.1007/s00004-017-0363-7
Gamba, Enrico (2012), "The mathematical ideas of Luca Pacioli depicted by Iacopo de' Barbari in the Doppio ritratto", in Emmer, Michele (ed.), Imagine Math, Springer, pp. 267–271, doi:10.1007/978-88-470-2427-4_25, ISBN 978-88-470-2427-4
Calvo-López, José; Alonso-Rodríguez, Miguel Ángel (February 2010), "Perspective versus stereotomy: From Quattrocento polyhedral rings to sixteenth-century Spanish torus vaults", Nexus Network Journal, 12 (1): 75–111, doi:10.1007/s00004-010-0018-4
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Montebelli, Vico (2015), "Luca Pacioli and perspective (part I)", Lettera Matematica, 3 (3): 135–141, doi:10.1007/s40329-015-0090-4, MR 3402538, S2CID 193533200
Ghomi, Mohammad (2018), "Dürer's unfolding problem for convex polyhedra" (PDF), Notices of the American Mathematical Society, 65 (1): 25–27, doi:10.1090/noti1609, MR 3726673
Field, J. V. (1979), "Kepler's star polyhedra", Vistas in Astronomy, 23 (2): 109–141, Bibcode:1979VA.....23..109F, doi:10.1016/0083-6656(79)90001-1, MR 0546797
Friedman, Michael (2018), A History of Folding in Mathematics: Mathematizing the Margins, Science Networks. Historical Studies, vol. 59, Birkhäuser, p. 71, doi:10.1007/978-3-319-72487-4, ISBN 978-3-319-72486-7
Francese, Christopher; Richeson, David (2007), "The flaw in Euler's proof of his polyhedral formula", The American Mathematical Monthly, 114 (4): 286–296, doi:10.1080/00029890.2007.11920417, MR 2281926, S2CID 10023787
Alexanderson, Gerald L. (2006), "About the cover: Euler and Königsberg's bridges: a historical view", American Mathematical Society, New Series, 43 (4): 567–573, doi:10.1090/S0273-0979-06-01130-X, MR 2247921
Eckmann, Beno (2006), "The Euler characteristic – a few highlights in its long history", Mathematical Survey Lectures 1943–2004, Springer, pp. 177–188, doi:10.1007/978-3-540-33791-1_15, ISBN 978-3-540-33791-1, MR 2269092
Zeeman, E. C. (July 2002), "On Hilbert's third problem", The Mathematical Gazette, 86 (506): 241–247, doi:10.2307/3621846, JSTOR 3621846, S2CID 125593771
Grünbaum, Branko (2007), "Graphs of polyhedra; polyhedra as graphs", Discrete Mathematics, 307 (3–5): 445–463, doi:10.1016/j.disc.2005.09.037, hdl:1773/2276, MR 2287486
Lim, Seng Poh; Haron, Habibollah (March 2012), "Surface reconstruction techniques: a review", Artificial Intelligence Review, 42 (1): 59–78, doi:10.1007/s10462-012-9329-z, S2CID 254232891
Mitchell, Joseph S. B.; Mount, David M.; Papadimitriou, Christos H. (1987), "The discrete geodesic problem", SIAM Journal on Computing, 16 (4): 647–668, doi:10.1137/0216045, MR 0899694
Teller, Seth J.; Hanrahan, Pat (1993), "Global visibility algorithms for illumination computations", in Whitton, Mary C. (ed.), Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1993, Anaheim, CA, USA, August 2–6, 1993, Association for Computing Machinery, pp. 239–246, doi:10.1145/166117.166148, ISBN 0-89791-601-8, S2CID 7957200
Rote, Günter (2011), "Realizing planar graphs as convex polytopes", in van Kreveld, Marc J.; Speckmann, Bettina (eds.), Graph Drawing – 19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 21–23, 2011, Revised Selected Papers, Lecture Notes in Computer Science, vol. 7034, Springer, pp. 238–241, doi:10.1007/978-3-642-25878-7_23, ISBN 978-3-642-25877-0

encyclopediaofmath.org

Matveev, S.V. (2001) [1994], "Polyhedron, abstract", Encyclopedia of Mathematics, EMS Press
Hazewinkel, M. (2001) [1994], "Dehn invariant", Encyclopedia of Mathematics, EMS Press

eudml.org

Sydler, J.-P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (in French), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371

gbv.de

O'Rourke, Joseph (1993), "Computational Geometry in C" (PDF), Computers in Physics, 9 (1): 113–116, Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371.

handle.net

hdl.handle.net

Grünbaum, Branko (2007), "Graphs of polyhedra; polyhedra as graphs", Discrete Mathematics, 307 (3–5): 445–463, doi:10.1016/j.disc.2005.09.037, hdl:1773/2276, MR 2287486
Cherchi, Gianmarco (February 2019), Polycube Optimization and Applications: From the Digital World to Manufacturing (Doctoral dissertation), University of Cagliari, hdl:11584/261570

harvard.edu

ui.adsabs.harvard.edu

O'Rourke, Joseph (1993), "Computational Geometry in C" (PDF), Computers in Physics, 9 (1): 113–116, Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371.
Schramm, Oded (1992-12-01), "How to cage an egg", Inventiones Mathematicae, 107 (1): 543–560, Bibcode:1992InMat.107..543S, doi:10.1007/BF01231901, ISSN 1432-1297.
Bridge, N.J. (1974), "Facetting the dodecahedron", Acta Crystallographica, A30 (4): 548–552, Bibcode:1974AcCrA..30..548B, doi:10.1107/S0567739474001306.
Coxeter, H. S. M. (January 1930), "The polytopes with regular-prismatic vertex figures", Philosophical Transactions of the Royal Society of London, Series A, 229 (670–680), The Royal Society: 329–425, Bibcode:1930RSPTA.229..329C, doi:10.1098/rsta.1930.0009
Field, J. V. (1979), "Kepler's star polyhedra", Vistas in Astronomy, 23 (2): 109–141, Bibcode:1979VA.....23..109F, doi:10.1016/0083-6656(79)90001-1, MR 0546797

jstor.org

Litchenberg, D. R. (1988), "Pyramids, Prisms, Antiprisms, and Deltahedra", The Mathematics Teacher, 81 (4): 261–265, JSTOR 27965792.
Cundy, H. Martyn (1952), "Deltahedra", Mathematical Gazette, 36: 263–266, doi:10.2307/3608204, JSTOR 3608204.
Taylor, Jean E. (1992), "Zonohedra and generalized zonohedra", American Mathematical Monthly, 99 (2): 108–111, doi:10.2307/2324178, JSTOR 2324178, MR 1144350.
Gardner, Martin (November 1966), "Mathematical Games: Is it possible to visualize a four-dimensional figure?", Scientific American, 215 (5): 138–143, doi:10.1038/scientificamerican1166-138, JSTOR 24931332
Friberg, Jöran (2000), "Mathematics at Ur in the Old Babylonian Period", Revue d'Assyriologie et d'archéologie orientale, 94 (2): 97–188, JSTOR 23281940
Eves, Howard (January 1969), "A geometry capsule concerning the five platonic solids", Historically Speaking, The Mathematics Teacher, 62 (1): 42–44, doi:10.5951/mt.62.1.0042, JSTOR 27958041
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Zeeman, E. C. (July 2002), "On Hilbert's third problem", The Mathematical Gazette, 86 (506): 241–247, doi:10.2307/3621846, JSTOR 3621846, S2CID 125593771

projecteuclid.org

Barnette, David (1973), "A proof of the lower bound conjecture for convex polytopes", Pacific Journal of Mathematics, 46 (2): 349–354, doi:10.2140/pjm.1973.46.349, MR 0328773

psu.edu

citeseerx.ist.psu.edu

Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics, vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487
Bruns, Winfried; Gubeladze, Joseph (2009), "Definition 1.1", Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer, p. 5, CiteSeerX 10.1.1.693.2630, doi:10.1007/b105283, ISBN 978-0-387-76355-2, MR 2508056.
Büeler, B.; Enge, A.; Fukuda, K. (2000), "Exact Volume Computation for Polytopes: A Practical Study", Polytopes — Combinatorics and Computation, pp. 131–154, CiteSeerX 10.1.1.39.7700, doi:10.1007/978-3-0348-8438-9_6, ISBN 978-3-7643-6351-2
Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry, 99 (1–2): 1–13, arXiv:0901.2989, CiteSeerX 10.1.1.243.7674, doi:10.1007/s00022-011-0061-7, MR 2823098, S2CID 17515249.

semanticscholar.org

api.semanticscholar.org

Inchbald, G. (2006), "Facetting diagrams", The Mathematical Gazette, 90 (518): 253–261, doi:10.1017/S0025557200179653, S2CID 233358800.
Sydler, J.-P. (1965), "Conditions nécessaires et suffisantes pour l'équivalence des polyèdres de l'espace euclidien à trois dimensions", Comment. Math. Helv. (in French), 40: 43–80, doi:10.1007/bf02564364, MR 0192407, S2CID 123317371
Debrunner, Hans E. (1980), "Über Zerlegungsgleichheit von Pflasterpolyedern mit Würfeln", Archiv der Mathematik (in German), 35 (6): 583–587, doi:10.1007/BF01235384, MR 0604258, S2CID 121301319.
Alexandrov, Victor (2010), "The Dehn invariants of the Bricard octahedra", Journal of Geometry, 99 (1–2): 1–13, arXiv:0901.2989, CiteSeerX 10.1.1.243.7674, doi:10.1007/s00022-011-0061-7, MR 2823098, S2CID 17515249.
Coxeter, H.S.M. (1985), "A special book review: M.C. Escher: His life and complete graphic work", The Mathematical Intelligencer, 7 (1): 59–69, doi:10.1007/BF03023010, S2CID 189887063 Coxeter's analysis of Stars is on pp. 61–62.
Gunn, Battiscombe; Peet, T. Eric (May 1929), "Four Geometrical Problems from the Moscow Mathematical Papyrus", The Journal of Egyptian Archaeology, 15 (1): 167–185, doi:10.1177/030751332901500130, S2CID 192278129
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Bréard, Andrea; Cook, Constance A. (December 2019), "Cracking bones and numbers: solving the enigma of numerical sequences on ancient Chinese artifacts", Archive for History of Exact Sciences, 74 (4): 313–343, doi:10.1007/s00407-019-00245-9, S2CID 253898304
Field, J. V. (1997), "Rediscovering the Archimedean polyhedra: Piero della Francesca, Luca Pacioli, Leonardo da Vinci, Albrecht Dürer, Daniele Barbaro, and Johannes Kepler", Archive for History of Exact Sciences, 50 (3–4): 241–289, doi:10.1007/BF00374595, JSTOR 41134110, MR 1457069, S2CID 118516740
Montebelli, Vico (2015), "Luca Pacioli and perspective (part I)", Lettera Matematica, 3 (3): 135–141, doi:10.1007/s40329-015-0090-4, MR 3402538, S2CID 193533200
Francese, Christopher; Richeson, David (2007), "The flaw in Euler's proof of his polyhedral formula", The American Mathematical Monthly, 114 (4): 286–296, doi:10.1080/00029890.2007.11920417, MR 2281926, S2CID 10023787
Zeeman, E. C. (July 2002), "On Hilbert's third problem", The Mathematical Gazette, 86 (506): 241–247, doi:10.2307/3621846, JSTOR 3621846, S2CID 125593771
Lim, Seng Poh; Haron, Habibollah (March 2012), "Surface reconstruction techniques: a review", Artificial Intelligence Review, 42 (1): 59–78, doi:10.1007/s10462-012-9329-z, S2CID 254232891
Teller, Seth J.; Hanrahan, Pat (1993), "Global visibility algorithms for illumination computations", in Whitton, Mary C. (ed.), Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1993, Anaheim, CA, USA, August 2–6, 1993, Association for Computing Machinery, pp. 239–246, doi:10.1145/166117.166148, ISBN 0-89791-601-8, S2CID 7957200

washington.edu

sites.math.washington.edu

Grünbaum, Branko (1999), "Acoptic polyhedra" (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 2021-08-30, retrieved 2022-07-01.

faculty.washington.edu

Grünbaum, Branko (2003), "Are your polyhedra the same as my polyhedra?" (PDF), in Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (eds.), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics, vol. 25, Berlin: Springer, pp. 461–488, CiteSeerX 10.1.1.102.755, doi:10.1007/978-3-642-55566-4_21, ISBN 978-3-642-62442-1, MR 2038487

digital.lib.washington.edu

Grünbaum, Branko (2009), "An enduring error" (PDF), Elemente der Mathematik, 64 (3): 89–101, doi:10.4171/EM/120, MR 2520469. Reprinted in Pitici, Mircea, ed. (2011), The Best Writing on Mathematics 2010, Princeton University Press, pp. 18–31.

web.archive.org

Grünbaum, Branko (1999), "Acoptic polyhedra" (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics, vol. 223, Providence, Rhode Island: American Mathematical Society, pp. 163–199, doi:10.1090/conm/223/03137, ISBN 978-0-8218-0674-6, MR 1661382, archived from the original (PDF) on 2021-08-30, retrieved 2022-07-01.
Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.

wias-berlin.de

Grünbaum, B.; Shephard, G.C. (1969), "Convex polytopes" (PDF), Bulletin of the London Mathematical Society, 1 (3): 257–300, doi:10.1112/blms/1.3.257, MR 0250188, archived from the original (PDF) on 2017-02-22, retrieved 2017-02-21. See in particular the bottom of page 260.

worldcat.org

search.worldcat.org

Schramm, Oded (1992-12-01), "How to cage an egg", Inventiones Mathematicae, 107 (1): 543–560, Bibcode:1992InMat.107..543S, doi:10.1007/BF01231901, ISSN 1432-1297.
Cox, David A. (2011), Toric varieties, John B. Little, Henry K. Schenck, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4819-7, OCLC 698027255
Stanley, Richard P. (1996), Combinatorics and commutative algebra (2nd ed.), Boston: Birkhäuser, ISBN 0-8176-3836-9, OCLC 33080168