Sphere packing (English Wikipedia)

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

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21doi.org

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15semanticscholar.org

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14arxiv.org

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7worldcat.org

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7harvard.edu

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3wolfram.com

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2princeton.edu

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2quantamagazine.org

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1hal.science

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1code.google.com

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1nih.gov

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1ghostarchive.org

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1americanscientist.org

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americanscientist.org

"The Science of Sticky Spheres". American Scientist. 6 February 2017. Retrieved 14 July 2020.

ams.org

mathscinet.ams.org

Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591
Torquato, S.; Stillinger, F. H. (2006), "New conjectural lower bounds on the optimal density of sphere packings", Experimental Mathematics, 15 (3): 307–331, arXiv:math/0508381, doi:10.1080/10586458.2006.10128964, MR 2264469, S2CID 9921359

ams.org

Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591

arxiv.org

Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. ISSN 1434-7636. S2CID 254106945.
Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184. S2CID 5704550.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438. S2CID 4420652.
Sloane, N. J. A. (1998). "The Sphere-Packing Problem". Documenta Mathematica. 3: 387–396. arXiv:math/0207256. Bibcode:2002math......7256S.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. S2CID 119286185.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. S2CID 119281758.
Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591
Torquato, S.; Stillinger, F. H. (2006), "New conjectural lower bounds on the optimal density of sphere packings", Experimental Mathematics, 15 (3): 307–331, arXiv:math/0508381, doi:10.1080/10586458.2006.10128964, MR 2264469, S2CID 9921359
Campos, Marcelo; Jenssen, Matthew; Michelen, Marcus; Sahasrabudhe, Julian (2023). "A new lower bound for sphere packing". arXiv:2312.10026 [math.MG].
de Laat, David; de Oliveira Filho, Fernando Mário; Vallentin, Frank (12 June 2012). "Upper bounds for packings of spheres of several radii". Forum of Mathematics, Sigma. 2. arXiv:1206.2608. doi:10.1017/fms.2014.24. S2CID 11082628.
Dennis, Robert; Corwin, Eric (2 September 2021). "Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities". Physical Review. 128 (1): 018002. arXiv:2006.11415. doi:10.1103/PhysRevLett.128.018002.
Kozma, R. T.; Szirmai, J. (2012). "Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types". Monatshefte für Mathematik. 168: 27–47. arXiv:1007.0722. doi:10.1007/s00605-012-0393-x. S2CID 119713174.
Bezdek, Karoly; Reid, Samuel (2013). "Contact Graphs of Sphere Packings Revisited". Journal of Geometry. 104 (1): 57–83. arXiv:1210.5756. doi:10.1007/s00022-013-0156-4. S2CID 14428585.

books.google.com

Conway, John H.; Sloane, Neil J. A. (1998). Sphere Packings, Lattices and Groups (3rd ed.). Springer Science & Business Media. ISBN 0-387-98585-9.

code.google.com

"Long-term storage for Google Code Project Hosting". Google Code Archive.

doi.org

Wu, Yugong; Fan, Zhigang; Lu, Yuzhu (1 May 2003). "Bulk and interior packing densities of random close packing of hard spheres". Journal of Materials Science. 38 (9): 2019–2025. doi:10.1023/A:1023597707363. ISSN 1573-4803. S2CID 137583828.
Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. ISSN 1434-7636. S2CID 254106945.
Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184. S2CID 5704550.
Chaikin, Paul (June 2007). "Random thoughts". Physics Today. 60 (6). American Institute of Physics: 8. Bibcode:2007PhT....60f...8C. doi:10.1063/1.2754580. ISSN 0031-9228.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438. S2CID 4420652.
Griffith, J.S. (1962). "Packing of equal 0-spheres". Nature. 196 (4856): 764–765. Bibcode:1962Natur.196..764G. doi:10.1038/196764a0. S2CID 4262056.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. S2CID 119286185.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. S2CID 119281758.
Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591
Torquato, S.; Stillinger, F. H. (2006), "New conjectural lower bounds on the optimal density of sphere packings", Experimental Mathematics, 15 (3): 307–331, arXiv:math/0508381, doi:10.1080/10586458.2006.10128964, MR 2264469, S2CID 9921359
O'Toole, P. I.; Hudson, T. S. (2011). "New High-Density Packings of Similarly Sized Binary Spheres". The Journal of Physical Chemistry C. 115 (39): 19037. doi:10.1021/jp206115p.
Hudson, D. R. (1949). "Density and Packing in an Aggregate of Mixed Spheres". Journal of Applied Physics. 20 (2): 154–162. Bibcode:1949JAP....20..154H. doi:10.1063/1.1698327.
Zong, C. (2002). "From deep holes to free planes". Bulletin of the American Mathematical Society. 39 (4): 533–555. doi:10.1090/S0273-0979-02-00950-3.
de Laat, David; de Oliveira Filho, Fernando Mário; Vallentin, Frank (12 June 2012). "Upper bounds for packings of spheres of several radii". Forum of Mathematics, Sigma. 2. arXiv:1206.2608. doi:10.1017/fms.2014.24. S2CID 11082628.
Dennis, Robert; Corwin, Eric (2 September 2021). "Dionysian Hard Sphere Packings Are Mechanically Stable at Vanishingly Low Densities". Physical Review. 128 (1): 018002. arXiv:2006.11415. doi:10.1103/PhysRevLett.128.018002.
Bowen, L.; Radin, C. (2002). "Densest Packing of Equal Spheres in Hyperbolic Space". Discrete and Computational Geometry. 29: 23–39. doi:10.1007/s00454-002-2791-7.
Böröczky, K. (1978). "Packing of spheres in spaces of constant curvature". Acta Mathematica Academiae Scientiarum Hungaricae. 32 (3–4): 243–261. doi:10.1007/BF01902361. S2CID 122561092.
Böröczky, K.; Florian, A. (1964). "Über die dichteste Kugelpackung im hyperbolischen Raum". Acta Mathematica Academiae Scientiarum Hungaricae. 15 (1–2): 237–245. doi:10.1007/BF01897041. S2CID 122081239.
Kozma, R. T.; Szirmai, J. (2012). "Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types". Monatshefte für Mathematik. 168: 27–47. arXiv:1007.0722. doi:10.1007/s00605-012-0393-x. S2CID 119713174.
Bezdek, Karoly; Reid, Samuel (2013). "Contact Graphs of Sphere Packings Revisited". Journal of Geometry. 104 (1): 57–83. arXiv:1210.5756. doi:10.1007/s00022-013-0156-4. S2CID 14428585.

emis.de

Marshall, G. W.; Hudson, T. S. (2010). "Dense binary sphere packings". Contributions to Algebra and Geometry. 51 (2): 337–344.

ghostarchive.org

Miller, Stephen D. (4 April 2016), The solution to the sphere packing problem in 24 dimensions via modular forms, Institute for Advanced Study, archived from the original on 21 December 2021. Video of an hour-long talk by one of Viazovska's co-authors explaining the new proofs.

hal.science

Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. ISSN 1434-7636. S2CID 254106945.

harvard.edu

ui.adsabs.harvard.edu

Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184. S2CID 5704550.
Chaikin, Paul (June 2007). "Random thoughts". Physics Today. 60 (6). American Institute of Physics: 8. Bibcode:2007PhT....60f...8C. doi:10.1063/1.2754580. ISSN 0031-9228.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438. S2CID 4420652.
Griffith, J.S. (1962). "Packing of equal 0-spheres". Nature. 196 (4856): 764–765. Bibcode:1962Natur.196..764G. doi:10.1038/196764a0. S2CID 4262056.
Sloane, N. J. A. (1998). "The Sphere-Packing Problem". Documenta Mathematica. 3: 387–396. arXiv:math/0207256. Bibcode:2002math......7256S.
Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Hudson, D. R. (1949). "Density and Packing in an Aggregate of Mixed Spheres". Journal of Applied Physics. 20 (2): 154–162. Bibcode:1949JAP....20..154H. doi:10.1063/1.1698327.

nih.gov

pubmed.ncbi.nlm.nih.gov

Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438. S2CID 4420652.

princeton.edu

annals.math.princeton.edu

Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. S2CID 119286185.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. S2CID 119281758.

quantamagazine.org

Klarreich, Erica (30 March 2016), "Sphere Packing Solved in Higher Dimensions", Quanta Magazine
Houston-Edwards, Kelsey (30 April 2024). "To Pack Spheres Tightly, Mathematicians Throw Them at Random". Quanta Magazine. Retrieved 30 April 2024.

semanticscholar.org

api.semanticscholar.org

Wu, Yugong; Fan, Zhigang; Lu, Yuzhu (1 May 2003). "Bulk and interior packing densities of random close packing of hard spheres". Journal of Materials Science. 38 (9): 2019–2025. doi:10.1023/A:1023597707363. ISSN 1573-4803. S2CID 137583828.
Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. ISSN 1434-7636. S2CID 254106945.
Torquato, S.; Stillinger, F. H. (2007). "Toward the jamming threshold of sphere packings: Tunneled crystals". Journal of Applied Physics. 102 (9): 093511–093511–8. arXiv:0707.4263. Bibcode:2007JAP...102i3511T. doi:10.1063/1.2802184. S2CID 5704550.
Song, C.; Wang, P.; Makse, H. A. (29 May 2008). "A phase diagram for jammed matter". Nature. 453 (7195): 629–632. arXiv:0808.2196. Bibcode:2008Natur.453..629S. doi:10.1038/nature06981. PMID 18509438. S2CID 4420652.
Griffith, J.S. (1962). "Packing of equal 0-spheres". Nature. 196 (4856): 764–765. Bibcode:1962Natur.196..764G. doi:10.1038/196764a0. S2CID 4262056.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. S2CID 119286185.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. S2CID 119281758.
Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591
Torquato, S.; Stillinger, F. H. (2006), "New conjectural lower bounds on the optimal density of sphere packings", Experimental Mathematics, 15 (3): 307–331, arXiv:math/0508381, doi:10.1080/10586458.2006.10128964, MR 2264469, S2CID 9921359
de Laat, David; de Oliveira Filho, Fernando Mário; Vallentin, Frank (12 June 2012). "Upper bounds for packings of spheres of several radii". Forum of Mathematics, Sigma. 2. arXiv:1206.2608. doi:10.1017/fms.2014.24. S2CID 11082628.
Böröczky, K. (1978). "Packing of spheres in spaces of constant curvature". Acta Mathematica Academiae Scientiarum Hungaricae. 32 (3–4): 243–261. doi:10.1007/BF01902361. S2CID 122561092.
Böröczky, K.; Florian, A. (1964). "Über die dichteste Kugelpackung im hyperbolischen Raum". Acta Mathematica Academiae Scientiarum Hungaricae. 15 (1–2): 237–245. doi:10.1007/BF01897041. S2CID 122081239.
Kozma, R. T.; Szirmai, J. (2012). "Optimally dense packings for fully asymptotic Coxeter tilings by horoballs of different types". Monatshefte für Mathematik. 168: 27–47. arXiv:1007.0722. doi:10.1007/s00605-012-0393-x. S2CID 119713174.
Bezdek, Karoly; Reid, Samuel (2013). "Contact Graphs of Sphere Packings Revisited". Journal of Geometry. 104 (1): 57–83. arXiv:1210.5756. doi:10.1007/s00022-013-0156-4. S2CID 14428585.

tandfonline.com

Torquato, S.; Stillinger, F. H. (2006), "New conjectural lower bounds on the optimal density of sphere packings", Experimental Mathematics, 15 (3): 307–331, arXiv:math/0508381, doi:10.1080/10586458.2006.10128964, MR 2264469, S2CID 9921359

wolfram.com

mathworld.wolfram.com

worldcat.org

search.worldcat.org

Wu, Yugong; Fan, Zhigang; Lu, Yuzhu (1 May 2003). "Bulk and interior packing densities of random close packing of hard spheres". Journal of Materials Science. 38 (9): 2019–2025. doi:10.1023/A:1023597707363. ISSN 1573-4803. S2CID 137583828.
Dai, Weijing; Reimann, Joerg; Hanaor, Dorian; Ferrero, Claudio; Gan, Yixiang (13 March 2019). "Modes of wall induced granular crystallisation in vibrational packing". Granular Matter. 21 (2): 26. arXiv:1805.07865. doi:10.1007/s10035-019-0876-8. ISSN 1434-7636. S2CID 254106945.
Chaikin, Paul (June 2007). "Random thoughts". Physics Today. 60 (6). American Institute of Physics: 8. Bibcode:2007PhT....60f...8C. doi:10.1063/1.2754580. ISSN 0031-9228.
Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 8". Annals of Mathematics. 185 (3): 991–1015. arXiv:1603.04246. doi:10.4007/annals.2017.185.3.7. ISSN 0003-486X. S2CID 119286185.
Cohn, Henry; Kumar, Abhinav; Miller, Stephen; Radchenko, Danylo; Viazovska, Maryna (1 January 2017). "The sphere packing problem in dimension 24". Annals of Mathematics. 185 (3): 1017–1033. arXiv:1603.06518. doi:10.4007/annals.2017.185.3.8. ISSN 0003-486X. S2CID 119281758.
Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595
Cohn, Henry (2017), "A conceptual breakthrough in sphere packing" (PDF), Notices of the American Mathematical Society, 64 (2): 102–115, arXiv:1611.01685, doi:10.1090/noti1474, ISSN 0002-9920, MR 3587715, S2CID 16124591

youtube.com

Miller, Stephen D. (4 April 2016), The solution to the sphere packing problem in 24 dimensions via modular forms, Institute for Advanced Study, archived from the original on 21 December 2021. Video of an hour-long talk by one of Viazovska's co-authors explaining the new proofs.

zbmath.org

Cohn, Henry; Kumar, Abhinav (2009), "Optimality and uniqueness of the Leech lattice among lattices", Annals of Mathematics, 170 (3): 1003–1050, arXiv:math.MG/0403263, doi:10.4007/annals.2009.170.1003, ISSN 1939-8980, MR 2600869, S2CID 10696627, Zbl 1213.11144 Cohn, Henry; Kumar, Abhinav (2004), "The densest lattice in twenty-four dimensions", Electronic Research Announcements of the American Mathematical Society, 10 (7): 58–67, arXiv:math.MG/0408174, Bibcode:2004math......8174C, doi:10.1090/S1079-6762-04-00130-1, ISSN 1079-6762, MR 2075897, S2CID 15874595