In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.
The currently densest known packing structure for regular tetrahedra is a double lattice of triangular bipyramids and fills 85.63% of space
Currently, the best lower bound achieved on the optimal packing fraction of regular tetrahedra is 85.63%.[1] Tetrahedra do not tile space,[2] and an upper bound below 100% (namely, 1 − (2.6...)·10−25) has been reported.[3]
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Chen, Elizabeth R.; Engel, Michael; Glotzer, Sharon C. (2010). "Dense crystalline dimer packings of regular tetrahedra". Discrete & Computational Geometry. 44 (2): 253–280. arXiv:1001.0586. doi:10.1007/s00454-010-9273-0. S2CID 18523116.
^Struik, D. J. (1925). "Het probleem 'De Impletione Loci'". Nieuw Archief voor Wiskunde. 2nd ser. 15: 121–134. JFM 52.0002.04.
^Simon Gravel; Veit Elser; Yoav Kallus (2010). "Upper bound on the packing density of regular tetrahedra and octahedra". Discrete & Computational Geometry. 46 (4): 799–818. arXiv:1008.2830. doi:10.1007/s00454-010-9304-x. S2CID 18908213.
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