Abstract
We construct a dense packing of regular tetrahedra, with packing density D>.7786157.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
’ \(A\rho\iota\sigma\tau o\tau\acute{\varepsilon}\lambda\eta\varsigma\) : \(\varPi\varepsilon\rho\grave{\iota}\) ’ \(O\upsilon\rho\alpha\nu o\tilde{\upsilon}\) . Translation: Boethius: Aristotelēs. De Caelo. Translation: Guthrie, W.K.C.: Aristotle. On Heavenly Bodies. Leob Classical Library, vol. 338. Harvard University Press, vol. 6 (1986)
Betke, U., Henk, M.: (FORTRAN computer program) lattice_packing.f (1999)
Betke, U., Henk, M.: Densest lattice packings of 3-polytopes. Comput. Geom. 16(3), 157–186 (2000)
Conway, J.H., Torquato, S.: Packing, tiling, and covering with tetrahedra. Proc. Natl. Acad. Sci. U.S.A. 103, 10612–10617 (2006)
Grömer, H.: Über die dichteste gitterförmige Lagerung kongruenter Tetraeder. Mon. Math. 66, 12–15 (1962)
Hales, T.C.: A proof of the Kepler conjecture. Ann. Math. 162, 1065–1185 (2005)
Hales, T.C., Ferguson, S.P.: Historical overview of the Kepler conjecture; A formulation of the Kepler conjecture; Sphere packings III: Extremal cases; Sphere packings IV: Detailed bounds; Sphere packings V: Pentahedral prisms; Sphere packings VI: Tame graphs and linear programs. Discrete Comput. Geom. 36(1), 5–265 (2006)
Hilbert, D.C.: Mathematische Probleme. Nachr. Ges. Wiss. Gött., Math. Phys. Kl. 3, 253–297 (1900). Translation: Hilbert, D.C.: Mathematical problems. Bull. Am. Math. Soc. 8, 437–479 (1902)
Hoylman, D.J.: The densest lattice packing of tetrahedra. Bull. Am. Math. Soc. 76, 135–137 (1970)
Hurley, A.C.: Some helical structures generated by reflexions. Aust. J. Phys. 38(3), 299–310 (1985)
Minkowski, H.: Geometrie der Zahlen. Teubner, Leipzig (1896). Reprint: Minkowski, H.: Geometrie der Zahlen. Chelsea (1953)
Senechal, M.: Which tetrahedra fill space? Math. Mag. 54(5), 227–243 (1981)
Struik, D.J.: De impletione loci. Nieuw Arch. Wiskd. 15, 121–134 (1925)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was partially supported by the NSF-RTG grant DMS-0502170.
Rights and permissions
About this article
Cite this article
Chen, E.R. A Dense Packing of Regular Tetrahedra. Discrete Comput Geom 40, 214–240 (2008). https://doi.org/10.1007/s00454-008-9101-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00454-008-9101-y