Cube (English Wikipedia)

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

refsWebsite

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20books.google.com

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20doi.org

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6ams.org

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5jstor.org

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4archive.org

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3semanticscholar.org

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2arxiv.org

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1zbmath.org

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1wiley.com

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1fau.edu

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1uniyar.ac.ru

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1handle.net

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1heldermann-verlag.de

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1andrewwinslow.com

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ams.org

mathscinet.ams.org

Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603. See table II, line 3.
Cundy, H. Martyn; Rollett, A.P. (1961). "3.2 Duality". Mathematical models (2nd ed.). Oxford: Clarendon Press. pp. 78–79. MR 0124167.
Erdahl, R. M. (1999). "Zonotopes, dicings, and Voronoi's conjecture on parallelohedra". European Journal of Combinatorics. 20 (6): 527–549. doi:10.1006/eujc.1999.0294. MR 1703597.. Voronoi conjectured that all tilings of higher dimensional spaces by translates of a single convex polytope are combinatorially equivalent to Voronoi tilings, and Erdahl proves this in the special case of zonotopes. But as he writes (p. 429), Voronoi's conjecture for dimensions at most four was already proven by Delaunay. For the classification of three-dimensional parallelohedra into these five types, see Grünbaum, Branko; Shephard, G. C. (1980). "Tilings with congruent tiles". Bulletin of the American Mathematical Society. New Series. 3 (3): 951–973. doi:10.1090/S0273-0979-1980-14827-2. MR 0585178.
In higher dimensions, however, there exist parallelopes that are not zonotopes. See e.g. Shephard, G. C. (1974). "Space-filling zonotopes". Mathematika. 21 (2): 261–269. doi:10.1112/S0025579300008652. MR 0365332.
Horvat, Boris; Pisanski, Tomaž (2010). "Products of unit distance graphs". Discrete Mathematics. 310 (12): 1783–1792. doi:10.1016/j.disc.2009.11.035. MR 2610282.

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.

andrewwinslow.com

Langerman, Stefan; Winslow, Andrew (2016). "Polycube unfoldings satisfying Conway's criterion" (PDF). 19th Japan Conference on Discrete and Computational Geometry, Graphs, and Games (JCDCG^3 2016).

archive.org

Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. p. 309. ISBN 978-0-521-55432-9.
Coxeter, H.S.M. (1973). Regular Polytopes (3rd ed.). New York: Dover Publications. pp. 122–123. See §1.8 Configurations.
Cromwell (1997), p. 55.
Heath, Thomas L. (1908). The Thirteen Books of Euclid's Elements (3rd ed.). Cambridge University Press. p. 262, 478, 480.

arxiv.org

Hasan, Masud; Hossain, Mohammad M.; López-Ortiz, Alejandro; Nusrat, Sabrina; Quader, Saad A.; Rahman, Nabila (2010). "Some New Equiprojective Polyhedra". arXiv:1009.2252 [cs.CG].
Diaz, Giovanna; O'Rourke, Joseph (2015). "Hypercube unfoldings that tile $\mathbb {R} ^{3}$ and $\mathbb {R} ^{2}$ ". arXiv:1512.02086 [cs.CG].

books.google.com

Mills, Steve; Kolf, Hillary (1999). Maths Dictionary. Heinemann. p. 16. ISBN 978-0-435-02474-1.
Herrmann, Diane L.; Sally, Paul J. (2013). Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory. Taylor & Francis. p. 252. ISBN 978-1-4665-5464-1.
Khattar, Dinesh (2008). Guide to Objective Arithmetic (2nd ed.). Pearson Education. p. 377. ISBN 978-81-317-1682-3.
Ball, Keith (2010). "High-dimensional geometry and its probabilistic analogues". In Gowers, Timothy (ed.). The Princeton Companion to Mathematics. Princeton University Press. p. 671. ISBN 9781400830398.
Erickson, Martin (2011). Beautiful Mathematics. Mathematical Association of America. p. 62. ISBN 978-1-61444-509-8.
Senechal, Marjorie (1989). "A Brief Introduction to Tilings". In Jarić, Marko (ed.). Introduction to the Mathematics of Quasicrystals. Academic Press. p. 12.
Calter, Paul; Calter, Michael (2011). Technical Mathematics. John Wiley & Sons. p. 197. ISBN 978-0-470-53492-2.
Alexandrov, A. D. (2005). "8.1 Parallelohedra". Convex Polyhedra. Springer. pp. 349–359.
Smith, James (2000). Methods of Geometry. John Wiley & Sons. p. 392. ISBN 978-1-118-03103-2.
Rudolph, Michael (2022). The Mathematics of Finite Networks: An Introduction to Operator Graph Theory. Cambridge University Press. p. 25. doi:10.1007/9781316466919 (inactive 2024-07-17). ISBN 9781316466919.{{cite book}}: CS1 maint: DOI inactive as of July 2024 (link)
Chartrand, Gary; Zhang, Ping (2012). A First Course in Graph Theory. Dover Publications. p. 25. ISBN 978-0-486-29730-9.
Pisanski, Tomaž; Servatius, Brigitte (2013). Configuration from a Graphical Viewpoint. Springer. p. 21. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4.
Livio, Mario (2003) [2002]. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (1st trade paperback ed.). New York City: Broadway Books. p. 147. ISBN 978-0-7679-0816-0.
Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. p. 84–89. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.
Cromwell (1997), pp. 81–82.
Linti, G. (2013). "Catenated Compounds - Group 13 [Al, Ga, In, Tl]". In Reedijk, J.; Poeppelmmeier, K. (eds.). Comprehensive Inorganic Chemistry II: From Elements to Applications. Newnes. p. 41. ISBN 978-0-08-096529-1.
Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Coxeter, H. S. M. (1968). The Beauty of Geometry: Twelve Essays. Dover Publications. p. 167. ISBN 978-0-486-40919-1. See table III.
Barnes, John (2012). Gems of Geometry (2nd ed.). Springer. p. 82. doi:10.1007/978-3-642-30964-9. ISBN 978-3-642-30964-9.
Lunnon, W. F. (1972). "Symmetry of Cubical and General Polyominoes". In Read, Ronald C. (ed.). Graph Theory and Computing. New York: Academic Press. pp. 101–108. ISBN 978-1-48325-512-5.

doi.org

Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603. See table II, line 3.
Jerrard, Richard P.; Wetzel, John E.; Yuan, Liping (April 2017). "Platonic passages". Mathematics Magazine. 90 (2). Washington, DC: Mathematical Association of America: 87–98. doi:10.4169/math.mag.90.2.87. S2CID 218542147.
Lützen, Jesper (2010). "The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of the Angle". Centaurus. 52 (1): 4–37. doi:10.1111/j.1600-0498.2009.00160.x.
Cunningham, Gabe; Pellicer, Daniel (2024). "Finite 3-orbit polyhedra in ordinary space, II". Boletín de la Sociedad Matemática Mexicana. 30 (32). doi:10.1007/s40590-024-00600-z. See p. 276.
McLean, K. Robin (1990). "Dungeons, dragons, and dice". The Mathematical Gazette. 74 (469): 243–256. doi:10.2307/3619822. JSTOR 3619822. S2CID 195047512. See p. 247.
Grünbaum, Branko (1997). "Isogonal Prismatoids". Discrete & Computational Geometry. 18 (1): 13–52. doi:10.1007/PL00009307.
Erdahl, R. M. (1999). "Zonotopes, dicings, and Voronoi's conjecture on parallelohedra". European Journal of Combinatorics. 20 (6): 527–549. doi:10.1006/eujc.1999.0294. MR 1703597.. Voronoi conjectured that all tilings of higher dimensional spaces by translates of a single convex polytope are combinatorially equivalent to Voronoi tilings, and Erdahl proves this in the special case of zonotopes. But as he writes (p. 429), Voronoi's conjecture for dimensions at most four was already proven by Delaunay. For the classification of three-dimensional parallelohedra into these five types, see Grünbaum, Branko; Shephard, G. C. (1980). "Tilings with congruent tiles". Bulletin of the American Mathematical Society. New Series. 3 (3): 951–973. doi:10.1090/S0273-0979-1980-14827-2. MR 0585178.
In higher dimensions, however, there exist parallelopes that are not zonotopes. See e.g. Shephard, G. C. (1974). "Space-filling zonotopes". Mathematika. 21 (2): 261–269. doi:10.1112/S0025579300008652. MR 0365332.
Jeon, Kyungsoon (2009). "Mathematics Hiding in the Nets for a CUBE". Teaching Children Mathematics. 15 (7): 394–399. doi:10.5951/TCM.15.7.0394. JSTOR 41199313.
Rudolph, Michael (2022). The Mathematics of Finite Networks: An Introduction to Operator Graph Theory. Cambridge University Press. p. 25. doi:10.1007/9781316466919 (inactive 2024-07-17). ISBN 9781316466919.{{cite book}}: CS1 maint: DOI inactive as of July 2024 (link)
Harary, F.; Hayes, J. P.; Wu, H.-J. (1988). "A survey of the theory of hypercube graphs". Computers & Mathematics with Applications. 15 (4): 277–289. doi:10.1016/0898-1221(88)90213-1. hdl:2027.42/27522.
Horvat, Boris; Pisanski, Tomaž (2010). "Products of unit distance graphs". Discrete Mathematics. 310 (12): 1783–1792. doi:10.1016/j.disc.2009.11.035. MR 2610282.
Pisanski, Tomaž; Servatius, Brigitte (2013). Configuration from a Graphical Viewpoint. Springer. p. 21. doi:10.1007/978-0-8176-8364-1. ISBN 978-0-8176-8363-4.
Inchbald, Guy (2006). "Facetting Diagrams". The Mathematical Gazette. 90 (518): 253–261. doi:10.1017/S0025557200179653. JSTOR 40378613.
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.
Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. p. 84–89. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.
Viana, Vera; Xavier, João Pedro; Aires, Ana Paula; Campos, Helena (2019). "Interactive Expansion of Achiral Polyhedra". In Cocchiarella, Luigi (ed.). ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics 40th Anniversary - Milan, Italy, August 3-7, 2018. Advances in Intelligent Systems and Computing. Vol. 809. Springer. p. 1123. doi:10.1007/978-3-319-95588-9. ISBN 978-3-319-95587-2. See Fig. 6.
Holme, A. (2010). Geometry: Our Cultural Heritage. Springer. doi:10.1007/978-3-642-14441-7. ISBN 978-3-642-14441-7.
Barnes, John (2012). Gems of Geometry (2nd ed.). Springer. p. 82. doi:10.1007/978-3-642-30964-9. ISBN 978-3-642-30964-9.
Hall, T. Proctor (1893). "The projection of fourfold figures on a three-flat". American Journal of Mathematics. 15 (2): 179–189. doi:10.2307/2369565. JSTOR 2369565.

fau.edu

forumgeom.fau.edu

Poo-Sung, Park, Poo-Sung (2016). "Regular polytope distances" (PDF). Forum Geometricorum. 16: 227–232.{{cite journal}}: CS1 maint: multiple names: authors list (link)

handle.net

hdl.handle.net

Harary, F.; Hayes, J. P.; Wu, H.-J. (1988). "A survey of the theory of hypercube graphs". Computers & Mathematics with Applications. 15 (4): 277–289. doi:10.1016/0898-1221(88)90213-1. hdl:2027.42/27522.

heldermann-verlag.de

Slobodan, Mišić; Obradović, Marija; Ðukanović, Gordana (2015). "Composite Concave Cupolae as Geometric and Architectural Forms" (PDF). Journal for Geometry and Graphics. 19 (1): 79–91.

jstor.org

French, Doug (1988). "Reflections on a Cube". Mathematics in School. 17 (4): 30–33. JSTOR 30214515.
McLean, K. Robin (1990). "Dungeons, dragons, and dice". The Mathematical Gazette. 74 (469): 243–256. doi:10.2307/3619822. JSTOR 3619822. S2CID 195047512. See p. 247.
Jeon, Kyungsoon (2009). "Mathematics Hiding in the Nets for a CUBE". Teaching Children Mathematics. 15 (7): 394–399. doi:10.5951/TCM.15.7.0394. JSTOR 41199313.
Inchbald, Guy (2006). "Facetting Diagrams". The Mathematical Gazette. 90 (518): 253–261. doi:10.1017/S0025557200179653. JSTOR 40378613.
Hall, T. Proctor (1893). "The projection of fourfold figures on a three-flat". American Journal of Mathematics. 15 (2): 179–189. doi:10.2307/2369565. JSTOR 2369565.

semanticscholar.org

api.semanticscholar.org

Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603. See table II, line 3.
Jerrard, Richard P.; Wetzel, John E.; Yuan, Liping (April 2017). "Platonic passages". Mathematics Magazine. 90 (2). Washington, DC: Mathematical Association of America: 87–98. doi:10.4169/math.mag.90.2.87. S2CID 218542147.
McLean, K. Robin (1990). "Dungeons, dragons, and dice". The Mathematical Gazette. 74 (469): 243–256. doi:10.2307/3619822. JSTOR 3619822. S2CID 195047512. See p. 247.

uniyar.ac.ru

dcglab.uniyar.ac.ru

Kozachok, Marina (2012). "Perfect prismatoids and the conjecture concerning with face numbers of centrally symmetric polytopes". Yaroslavl International Conference "Discrete Geometry" dedicated to the centenary of A.D.Alexandrov (Yaroslavl, August 13-18, 2012) (PDF). P.G. Demidov Yaroslavl State University, International B.N. Delaunay Laboratory. pp. 46–49.

wiley.com

onlinelibrary.wiley.com

Lützen, Jesper (2010). "The Algebra of Geometric Impossibility: Descartes and Montucla on the Impossibility of the Duplication of the Cube and the Trisection of the Angle". Centaurus. 52 (1): 4–37. doi:10.1111/j.1600-0498.2009.00160.x.

zbmath.org

Johnson, Norman W. (1966). "Convex polyhedra with regular faces". Canadian Journal of Mathematics. 18: 169–200. doi:10.4153/cjm-1966-021-8. MR 0185507. S2CID 122006114. Zbl 0132.14603. See table II, line 3.