多面体 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "多面体" in Chinese language version.

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13doi.org

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ams.org

Lakatos, Imre, Worrall, John; Zahar, Elie , 编, Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press: 16, 2015, ISBN 978-1-107-53405-6, MR 3469698, doi:10.1017/CBO9781316286425, definitions are frequently proposed and argued about .
Cromwell, Peter R., Polyhedra, Cambridge: Cambridge University Press, 1997, 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, Acoptic polyhedra (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics 223, Providence, Rhode Island: American Mathematical Society: 163–199, 1999 [2023-11-15], ISBN 978-0-8218-0674-6, MR 1661382, doi:10.1090/conm/223/03137, （原始内容 (PDF)存档于2021-08-30） .
Bokowski, J.; Guedes de Oliveira, A., On the generation of oriented matroids, Discrete and Computational Geometry, 2000, 24 (2–3): 197–208, MR 1756651, doi:10.1007/s004540010027  .
Burgiel, H.; Stanton, D., Realizations of regular abstract polyhedra of types {3,6} and {6,3}, Discrete and Computational Geometry, 2000, 24 (2–3): 241–255, MR 1758047, doi:10.1007/s004540010030  .
Grünbaum, Branko, Are your polyhedra the same as my polyhedra? (PDF), Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003 [2023-11-15], CiteSeerX 10.1.1.102.755 , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21, （原始内容 (PDF)存档于2016-12-21）
Grünbaum, Branko, Convex Polytopes, Graduate Texts in Mathematics 221 2nd, New York: Springer-Verlag: 26, 2003, ISBN 978-0-387-00424-2, MR 1976856, doi:10.1007/978-1-4613-0019-9 .
Bruns, Winfried; Gubeladze, Joseph, Definition 1.1, Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer: 5, 2009, CiteSeerX 10.1.1.693.2630 , ISBN 978-0-387-76355-2, MR 2508056, doi:10.1007/b105283 .
Richeson, David S., Euler's Gem: The polyhedron formula and the birth of topology, Princeton, NJ: Princeton University Press, 2008, ISBN 978-0-691-12677-7, MR 2440945 , pp. 157, 180.
Cundy, H. Martyn; Rollett, A.P., 3.2 Duality, Mathematical models 2nd, Oxford: Clarendon Press: 78–79, 1961, MR 0124167 .
Grünbaum, B.; Shephard, G.C., Convex polytopes (PDF), Bulletin of the London Mathematical Society, 1969, 1 (3): 257–300 [2017-02-21], MR 0250188, doi:10.1112/blms/1.3.257, （原始内容 (PDF)存档于2017-02-22） . See in particular the bottom of page 260.
Barnette, David, A proof of the lower bound conjecture for convex polytopes, Pacific Journal of Mathematics, 1973, 46 (2): 349–354 [2023-11-16], MR 0328773, doi:10.2140/pjm.1973.46.349, （原始内容存档于2020-08-20）

archive.org

McMullen, Peter; Schulte, Egon, Abstract Regular Polytopes 1st, Cambridge University Press, December 2002, ISBN 0-521-81496-0

books.google.com

Bruns, Winfried; Gubeladze, Joseph, Definition 1.1, Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer: 5, 2009, CiteSeerX 10.1.1.693.2630 , ISBN 978-0-387-76355-2, MR 2508056, doi:10.1007/b105283 .
Peirce, Charles S., Eisele, Carolyn , 编, The New Elements of Mathematics, Volume II: Algebra and Geometry, Mouton Publishers & Humanities Press: 297, 1976 [2023-11-15], ISBN 9783110818840, （原始内容存档于2023-04-07）
O'Keefe, Michael; Hyde, Bruce G., Crystal Structures: Patterns and Symmetry, Dover Publications: 134, 2020, ISBN 9780486836546
Coxeter, H. S. M., Regular Polytopes, Methuen: 16, 1947

bridgesmathart.org

archive.bridgesmathart.org

Luotoniemi, Taneli, Crooked houses: Visualizing the polychora with hyperbolic patchwork, Swart, David; Séquin, Carlo H.; Fenyvesi, Kristóf (编), Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, Phoenix, Arizona: Tessellations Publishing: 17–24, 2017 [2023-11-16], ISBN 978-1-938664-22-9, （原始内容存档于2023-08-13）

doi.org

Lakatos, Imre, Worrall, John; Zahar, Elie , 编, Proofs and Refutations: The logic of mathematical discovery, Cambridge Philosophy Classics, Cambridge: Cambridge University Press: 16, 2015, ISBN 978-1-107-53405-6, MR 3469698, doi:10.1017/CBO9781316286425, definitions are frequently proposed and argued about .
Loeb, Arthur L., Polyhedra: Surfaces or solids?, Senechal, Marjorie (编), Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination 2nd, Springer: 65–75, 2013, doi:10.1007/978-0-387-92714-5_5
O'Rourke, Joseph, Computational Geometry in C (PDF), Computers in Physics, 1993, 9 (1): 113–116 [2023-11-15], Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371, （原始内容存档 (PDF)于2023-07-14） .
Grünbaum, Branko, Acoptic polyhedra (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics 223, Providence, Rhode Island: American Mathematical Society: 163–199, 1999 [2023-11-15], ISBN 978-0-8218-0674-6, MR 1661382, doi:10.1090/conm/223/03137, （原始内容 (PDF)存档于2021-08-30） .
Bokowski, J.; Guedes de Oliveira, A., On the generation of oriented matroids, Discrete and Computational Geometry, 2000, 24 (2–3): 197–208, MR 1756651, doi:10.1007/s004540010027  .
Burgiel, H.; Stanton, D., Realizations of regular abstract polyhedra of types {3,6} and {6,3}, Discrete and Computational Geometry, 2000, 24 (2–3): 241–255, MR 1758047, doi:10.1007/s004540010030  .
Grünbaum, Branko, Are your polyhedra the same as my polyhedra? (PDF), Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003 [2023-11-15], CiteSeerX 10.1.1.102.755 , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21, （原始内容 (PDF)存档于2016-12-21）
Grünbaum, Branko, Convex Polytopes, Graduate Texts in Mathematics 221 2nd, New York: Springer-Verlag: 26, 2003, ISBN 978-0-387-00424-2, MR 1976856, doi:10.1007/978-1-4613-0019-9 .
Bruns, Winfried; Gubeladze, Joseph, Definition 1.1, Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer: 5, 2009, CiteSeerX 10.1.1.693.2630 , ISBN 978-0-387-76355-2, MR 2508056, doi:10.1007/b105283 .
Ringel, Gerhard, Classification of surfaces, Map Color Theorem, Springer: 34–53, 1974, doi:10.1007/978-3-642-65759-7_3
Grünbaum, B.; Shephard, G.C., Convex polytopes (PDF), Bulletin of the London Mathematical Society, 1969, 1 (3): 257–300 [2017-02-21], MR 0250188, doi:10.1112/blms/1.3.257, （原始内容 (PDF)存档于2017-02-22） . See in particular the bottom of page 260.
Barnette, David, A proof of the lower bound conjecture for convex polytopes, Pacific Journal of Mathematics, 1973, 46 (2): 349–354 [2023-11-16], MR 0328773, doi:10.2140/pjm.1973.46.349, （原始内容存档于2020-08-20）
Coxeter, H. S. M., The polytopes with regular-prismatic vertex figures, Philosophical Transactions of the Royal Society of London, Series A (The Royal Society), January 1930, 229 (670–680): 329–425, doi:10.1098/rsta.1930.0009

encyclopediaofmath.org

Matveev, S.V., Polyhedron, abstract, Hazewinkel, Michiel (编), 数学百科全书, Springer, 2001, ISBN 978-1-55608-010-4

gbv.de

O'Rourke, Joseph, Computational Geometry in C (PDF), Computers in Physics, 1993, 9 (1): 113–116 [2023-11-15], Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371, （原始内容存档 (PDF)于2023-07-14） .

google.com.tw

books.google.com.tw

Elwes, R. and Elwes, R. Maths 1001: Absolutely Everything That Matters in Mathematics. Quercus. 2017 [2022-07-10]. ISBN 9781786486950. （原始内容存档于2022-07-13）.

harvard.edu

ui.adsabs.harvard.edu

O'Rourke, Joseph, Computational Geometry in C (PDF), Computers in Physics, 1993, 9 (1): 113–116 [2023-11-15], Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371, （原始内容存档 (PDF)于2023-07-14） .

mathopenref.com

Definition and properties of convex polygons with interactive animation.. [2020-03-03]. （原始内容存档于2017-10-17）.

projecteuclid.org

Barnette, David, A proof of the lower bound conjecture for convex polytopes, Pacific Journal of Mathematics, 1973, 46 (2): 349–354 [2023-11-16], MR 0328773, doi:10.2140/pjm.1973.46.349, （原始内容存档于2020-08-20）

psu.edu

citeseerx.ist.psu.edu

Grünbaum, Branko, Are your polyhedra the same as my polyhedra? (PDF), Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003 [2023-11-15], CiteSeerX 10.1.1.102.755 , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21, （原始内容 (PDF)存档于2016-12-21）
Bruns, Winfried; Gubeladze, Joseph, Definition 1.1, Polytopes, Rings, and K-theory, Springer Monographs in Mathematics, Dordrecht: Springer: 5, 2009, CiteSeerX 10.1.1.693.2630 , ISBN 978-0-387-76355-2, MR 2508056, doi:10.1007/b105283 .

springer.com

link.springer.com

Grünbaum, B. Polyhedra with Hollow Faces. Tibor Bisztriczky; Peter McMullen; Rolf Schneider; Alfred Weiss (编). Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational. Springer. 1994: 43–70 [2014-10-23]. ISBN 978-94-010-4398-4. （原始内容存档于2020-09-18）.

washington.edu

sites.math.washington.edu

Grünbaum, Branko, Acoptic polyhedra (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics 223, Providence, Rhode Island: American Mathematical Society: 163–199, 1999 [2023-11-15], ISBN 978-0-8218-0674-6, MR 1661382, doi:10.1090/conm/223/03137, （原始内容 (PDF)存档于2021-08-30） .

math.washington.edu

Grünbaum, Branko, Are your polyhedra the same as my polyhedra? (PDF), Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003 [2023-11-15], CiteSeerX 10.1.1.102.755 , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21, （原始内容 (PDF)存档于2016-12-21）

web.archive.org

Grünbaum, B. Polyhedra with Hollow Faces. Tibor Bisztriczky; Peter McMullen; Rolf Schneider; Alfred Weiss (编). Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational. Springer. 1994: 43–70 [2014-10-23]. ISBN 978-94-010-4398-4. （原始内容存档于2020-09-18）.
Elwes, R. and Elwes, R. Maths 1001: Absolutely Everything That Matters in Mathematics. Quercus. 2017 [2022-07-10]. ISBN 9781786486950. （原始内容存档于2022-07-13）.
O'Rourke, Joseph, Computational Geometry in C (PDF), Computers in Physics, 1993, 9 (1): 113–116 [2023-11-15], Bibcode:1995ComPh...9...55O, doi:10.1063/1.4823371, （原始内容存档 (PDF)于2023-07-14） .
Grünbaum, Branko, Acoptic polyhedra (PDF), Advances in discrete and computational geometry (South Hadley, MA, 1996), Contemporary Mathematics 223, Providence, Rhode Island: American Mathematical Society: 163–199, 1999 [2023-11-15], ISBN 978-0-8218-0674-6, MR 1661382, doi:10.1090/conm/223/03137, （原始内容 (PDF)存档于2021-08-30） .
Grünbaum, Branko, Are your polyhedra the same as my polyhedra? (PDF), Aronov, Boris; Basu, Saugata; Pach, János; Sharir, Micha (编), Discrete and Computational Geometry: The Goodman–Pollack Festschrift, Algorithms and Combinatorics 25, Berlin: Springer: 461–488, 2003 [2023-11-15], CiteSeerX 10.1.1.102.755 , ISBN 978-3-642-62442-1, MR 2038487, doi:10.1007/978-3-642-55566-4_21, （原始内容 (PDF)存档于2016-12-21）
Definition and properties of convex polygons with interactive animation.. [2020-03-03]. （原始内容存档于2017-10-17）.
Weisstein, Eric W. (编). Polyhedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. [2023-11-26]. （原始内容存档于2019-04-16）（英语）.
Peirce, Charles S., Eisele, Carolyn , 编, The New Elements of Mathematics, Volume II: Algebra and Geometry, Mouton Publishers & Humanities Press: 297, 1976 [2023-11-15], ISBN 9783110818840, （原始内容存档于2023-04-07）
The Tetrahemihexahedron. home.xs4all.nl. [2021-07-24]. （原始内容存档于2021-06-10）.
Grünbaum, B.; Shephard, G.C., Convex polytopes (PDF), Bulletin of the London Mathematical Society, 1969, 1 (3): 257–300 [2017-02-21], MR 0250188, doi:10.1112/blms/1.3.257, （原始内容 (PDF)存档于2017-02-22） . See in particular the bottom of page 260.
Barnette, David, A proof of the lower bound conjecture for convex polytopes, Pacific Journal of Mathematics, 1973, 46 (2): 349–354 [2023-11-16], MR 0328773, doi:10.2140/pjm.1973.46.349, （原始内容存档于2020-08-20）
Luotoniemi, Taneli, Crooked houses: Visualizing the polychora with hyperbolic patchwork, Swart, David; Séquin, Carlo H.; Fenyvesi, Kristóf (编), Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture, Phoenix, Arizona: Tessellations Publishing: 17–24, 2017 [2023-11-16], ISBN 978-1-938664-22-9, （原始内容存档于2023-08-13）

wias-berlin.de

Grünbaum, B.; Shephard, G.C., Convex polytopes (PDF), Bulletin of the London Mathematical Society, 1969, 1 (3): 257–300 [2017-02-21], MR 0250188, doi:10.1112/blms/1.3.257, （原始内容 (PDF)存档于2017-02-22） . See in particular the bottom of page 260.

wikipedia.org

en.wikipedia.org

Grünbaum, B. Polyhedra with Hollow Faces. Tibor Bisztriczky; Peter McMullen; Rolf Schneider; Alfred Weiss (编). Proceedings of the NATO Advanced Study Institute on Polytopes: Abstract, Convex and Computational. Springer. 1994: 43–70 [2014-10-23]. ISBN 978-94-010-4398-4. （原始内容存档于2020-09-18）.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. (编). Polyhedron. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. [2023-11-26]. （原始内容存档于2019-04-16）（英语）.

xs4all.nl

westy31.home.xs4all.nl

The Tetrahemihexahedron. home.xs4all.nl. [2021-07-24]. （原始内容存档于2021-06-10）.