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==Packing in infinite space==
Many of these problems, when the container size is increased in all directions, become equivalent to the problem of packing objects as densely as possible in infinite [[Euclidean space]]. This problem is relevant to a number of scientific disciplines, and has received significant attention. The [[Kepler conjecture]] postulated an optimal solution for [[sphere packing|packing spheres]] hundreds of years before it was [[mathematical proof|proven]] correct by [[Thomas Callister Hales]]. Many other shapes have received attention, including ellipsoids,<ref>{{Cite journal | last1 = Donev | first1 = A. | last2 = Stillinger | first2 = F. | last3 = Chaikin | first3 = P. | last4 = Torquato | first4 = S. | title = Unusually Dense Crystal Packings of Ellipsoids | doi = 10.1103/PhysRevLett.92.255506 | journal = Physical Review Letters | volume = 92 | issue = 25 | year = 2004 | pmid = 15245027|arxiv = cond-mat/0403286 |bibcode = 2004PhRvL..92y5506D | page=255506| s2cid = 7982407 }}</ref> [[Platonic solid|Platonic]] and [[Archimedean solid]]s<ref name="Torquato"/> including [[tetrahedron packing|tetrahedra]],<ref>{{Cite journal | doi = 10.1038/nature08641 | last1 = Haji-Akbari | first1 = A. | last2 = Engel | first2 = M. | last3 = Keys | first3 = A. S. | last4 = Zheng | pmid = 20010683 | first4 = X. | last5 = Petschek | first5 = R. G. | last6 = Palffy-Muhoray | first6 = P. | last7 = Glotzer | first7 = S. C. | title = Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra | year = 2009 | journal = Nature | volume = 462 | issue = 7274 | pages = 773–777 |bibcode = 2009Natur.462..773H |arxiv = 1012.5138 | s2cid = 4412674 }}</ref><ref>{{Cite journal | last1 = Chen | first1 = E. R. | last2 = Engel | first2 = M. | last3 = Glotzer | first3 = S. C. | title = Dense Crystalline Dimer Packings of Regular Tetrahedra | journal = [[Discrete & Computational Geometry]] | volume = 44 | issue = 2 | pages = 253–280 | year = 2010 | doi = 10.1007/s00454-010-9273-0| doi-access=free | arxiv = 1001.0586 | bibcode = 2010arXiv1001.0586C | s2cid = 18523116 }}</ref> [[Tripod packing|tripods]] (unions of [[cube]]s along three positive axis-parallel rays),<ref>{{citation|last=Stein|first=Sherman K.|author-link= Sherman K. Stein |date=March 1995|department=Mathematical entertainments|doi=10.1007/bf03024896|issue=2|journal=[[The Mathematical Intelligencer]]|pages=37–39|title=Packing tripods|volume=17|s2cid=124703268}}. Reprinted in {{citation|last=Gale|first=David|editor1-first=David|editor1-last=Gale|doi=10.1007/978-1-4612-2192-0|isbn=0-387-98272-8|mr=1661863|pages=131–136|publisher=Springer-Verlag|title=Tracking the Automatic ANT|year=1998}}</ref> and unequal-sphere dimers.<ref>{{Cite journal | last1 = Hudson | first1 = T. S. | last2 = Harrowell | first2 = P. | doi = 10.1088/0953-8984/23/19/194103 | pmid = 21525553 | title = Structural searches using isopointal sets as generators: Densest packings for binary hard sphere mixtures | journal = Journal of Physics: Condensed Matter | volume = 23 | issue = 19 | pages = 194103 | year = 2011 | bibcode = 2011JPCM...23s4103H | s2cid = 25505460 }}</ref>
===Hexagonal packing of circles===
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