{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T04:35:39Z","timestamp":1773462939651,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,7,17]],"date-time":"2010-07-17T00:00:00Z","timestamp":1279324800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2010,9]]},"DOI":"10.1007\/s00454-010-9273-0","type":"journal-article","created":{"date-parts":[[2010,7,16]],"date-time":"2010-07-16T09:51:07Z","timestamp":1279273867000},"page":"253-280","source":"Crossref","is-referenced-by-count":96,"title":["Dense Crystalline Dimer Packings of Regular Tetrahedra"],"prefix":"10.1007","volume":"44","author":[{"given":"Elizabeth R.","family":"Chen","sequence":"first","affiliation":[]},{"given":"Michael","family":"Engel","sequence":"additional","affiliation":[]},{"given":"Sharon C.","family":"Glotzer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2010,7,17]]},"reference":[{"key":"9273_CR1","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1126\/science.1128045","volume":"314","author":"Z.Y. Tang","year":"2006","unstructured":"Tang, Z.Y., Zhang, Z.L., Wang, Y., Glotzer, S.C., Kotov, N.A.: Spontaneous self-assembly of CdTe nanocrystals into free-floating sheets. Science 314, 274\u2013278 (2006)","journal-title":"Science"},{"key":"9273_CR2","doi-asserted-by":"crossref","first-page":"1670","DOI":"10.1021\/nl0706300","volume":"7","author":"Z.-L. Zhang","year":"2007","unstructured":"Zhang, Z.-L., Tang, Z.-Y., Kotov, N.A., Glotzer, S.C.: Self-assembly of CdTe nanoparticles into wires and sheets. Nano Letters 7, 1670\u20131675 (2007)","journal-title":"Nano Letters"},{"key":"9273_CR3","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1126\/science.1177218","volume":"327","author":"S. Srivastava","year":"2010","unstructured":"Srivastava, S., Santos, A., Critchley, K., Kim, K.-S., Podsiadlo, P., Sun, K., Lee, J., Lilly, G.D., Glotzer, S.C., Kotov, N.A.: Light-controlled self-assembly of semi-conductor nanoparticles into twisted ribbons. Science 327, 1355\u20131359 (2010)","journal-title":"Science"},{"key":"9273_CR4","unstructured":"Chen, E.R.: A picturebook of tetrahedral packings. Ph.D. Dissertation, University of Michigan (2010)"},{"key":"9273_CR5","first-page":"121","volume":"15","author":"D.J. Struik","year":"1925","unstructured":"Struik, D.J.: De impletione loci. Nieuw Arch. Wiskd. 15, 121\u2013134 (1925)","journal-title":"Nieuw Arch. Wiskd."},{"key":"9273_CR6","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1080\/0025570X.1981.11976933","volume":"54","author":"M. Senechal","year":"1981","unstructured":"Senechal, M.: Which tetrahedra fill space? Math. Mag. 54, 227\u2013243 (1981)","journal-title":"Math. Mag."},{"key":"9273_CR7","volume-title":"Geometrie der Zahlen","author":"H. Minkowski","year":"1896","unstructured":"Minkowski, H.: Geometrie der Zahlen. Teubner, Leipzig (1896)"},{"key":"9273_CR8","unstructured":"Minkowski, H.: Dichteste gitterf\u00f6rmige Lagerung kongruenter K\u00f6rper. Nachr. Ges. Wiss. G\u00f6tt. 311\u2013355 (1904)"},{"key":"9273_CR9","first-page":"253","volume":"3","author":"D.C. Hilbert","year":"1900","unstructured":"Hilbert, D.C.: Mathematische Probleme. Nachr. Ges. Wiss. G\u00f6tt., Math.-Phys. Kl. 3, 253\u2013297 (1900)","journal-title":"Nachr. Ges. Wiss. G\u00f6tt., Math.-Phys. Kl."},{"key":"9273_CR10","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/BF01418874","volume":"66","author":"H. Gr\u00f6mer","year":"1962","unstructured":"Gr\u00f6mer, H.: \u00dcber die dichteste gitterf\u00f6rmige Lagerung kongruenter Tetraeder. Monatshefte Math. 66, 12\u201315 (1962)","journal-title":"Monatshefte Math."},{"key":"9273_CR11","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1090\/S0002-9904-1970-12400-4","volume":"76","author":"D.J. Hoylman","year":"1970","unstructured":"Hoylman, D.J.: The densest lattice packing of tetrahedra. Bull. Am. Math. Soc. 76, 135\u2013137 (1970)","journal-title":"Bull. Am. Math. Soc."},{"key":"9273_CR12","volume-title":"The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems","author":"M. Gardner","year":"2001","unstructured":"Gardner, M.: The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems. Norton, New York (2001), 135\u00a0pp."},{"key":"9273_CR13","doi-asserted-by":"crossref","first-page":"1065","DOI":"10.4007\/annals.2005.162.1065","volume":"162","author":"T.C. Hales","year":"2005","unstructured":"Hales, T.C.: A proof of the Kepler conjecture. Ann. Math. 162, 1065\u20131185 (2005)","journal-title":"Ann. Math."},{"key":"9273_CR14","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/S0925-7721(00)00007-9","volume":"16","author":"U. Betke","year":"2000","unstructured":"Betke, U., Henk, M.: Densest lattice packings of 3-polytopes. Comput. Geom. 16, 157\u2013186 (2000)","journal-title":"Comput. Geom."},{"key":"9273_CR15","doi-asserted-by":"crossref","first-page":"10612","DOI":"10.1073\/pnas.0601389103","volume":"103","author":"J.H. Conway","year":"2006","unstructured":"Conway, J.H., Torquato, S.: Packing, tiling and covering with tetrahedra. Proc. Natl. Acad. Sci. USA 103, 10612\u201310617 (2006)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"9273_CR16","unstructured":"Chaikin, P., Wang, S., Jaoshvili, A.: Packing of tetrahedral and other dice. In: American Physical Society March Meeting, Denver, CO, paper S29.00010, 2007"},{"key":"9273_CR17","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.104.185501","volume":"104","author":"A. Jaoshvili","year":"2010","unstructured":"Jaoshvili, A., Esakia, A., Porrati, M., Chaikin, P.M.: Experiments on the random packing of tetrahedral dice. Phys. Rev. Lett. 104, 185501 (2010). doi: 10.1103\/PhysRevLett.104.185501","journal-title":"Phys. Rev. Lett."},{"key":"9273_CR18","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1007\/s00454-008-9101-y","volume":"40","author":"E.R. Chen","year":"2008","unstructured":"Chen, E.R.: A dense packing of regular tetrahedra. Discrete Comput. Geom. 40, 214\u2013240 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"9273_CR19","unstructured":"Haji-Akbari, A., Engel, M., Keys, A.S., Zheng, X.Y., Petschek, R., Palffy-Muhoray, P., Glotzer, S.C.: Dense packings of hard tetrahedra. In: American Physical Society March Meeting, Pittsburgh, PA, paper X9.00009, 2009"},{"key":"9273_CR20","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1038\/nature08239","volume":"460","author":"S. Torquato","year":"2009","unstructured":"Torquato, S., Jiao, Y.: Dense packings of the Platonic and Archimedean solids. Nature 460, 876\u2013879 (2009)","journal-title":"Nature"},{"key":"9273_CR21","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1038\/nature08641","volume":"462","author":"A. Haji-Akbari","year":"2009","unstructured":"Haji-Akbari, A., Engel, M., Keys, A.S., Zheng, X.Y., Petschek, R.G., Palffy-Muhoray, P., Glotzer, S.C.: Disordered, quasicrystalline, and crystalline phases of densely packed tetrahedra. Nature 462, 773\u2013777 (2009)","journal-title":"Nature"},{"key":"9273_CR22","author":"Y. Kallus","year":"2010","unstructured":"Kallus, Y., Elser, V., Gravel, S.: Dense periodic packings of tetrahedra with a small repeating units. Discrete Comput. Geom. (2010). doi: 10.1007\/s00454-010-9254-3 . arXiv:0910.5226 (2009)","journal-title":"Discrete Comput. Geom."},{"key":"9273_CR23","doi-asserted-by":"crossref","unstructured":"Torquato, S., Jiao, Y.: Analytical constructions of a family of dense tetrahedron packings and the role of symmetry. arXiv:0912.4210v3 (2009)","DOI":"10.1103\/PhysRevE.81.041310"},{"key":"9273_CR24","volume-title":"International Tables for Crystallography, Volume A: Space Group Symmetry","year":"2002","unstructured":"Hahn, T. (ed.): International Tables for Crystallography, Volume A: Space Group Symmetry, 5th edn. Springer, Berlin (2002)","edition":"5"},{"key":"9273_CR25","volume-title":"Understanding Molecular Simulation: From Algorithms to Applications","author":"D. Frenkel","year":"2001","unstructured":"Frenkel, D., Smit, B.: Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, New York (2001)"},{"key":"9273_CR26","unstructured":"http:\/\/glotzerlab.engin.umich.edu\/wiki\/public\/index.php\/Tetrahedra"},{"key":"9273_CR27","doi-asserted-by":"crossref","unstructured":"Chen, E.R., Engel, M., Glotzer, S.C.: Dense crystalline dimer packings of regular tetrahedra. Supplementary info in arXiv:1001.0586 (2010)","DOI":"10.1007\/s00454-010-9273-0"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-010-9273-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-010-9273-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-010-9273-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T00:25:44Z","timestamp":1559262344000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-010-9273-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,17]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["9273"],"URL":"https:\/\/doi.org\/10.1007\/s00454-010-9273-0","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,17]]}}}