Tetrahedron packing

Tetrahedron packing

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. A 2006 study by Conway and Torquato showed that a packing fraction of over 71.65598% can be obtained, but they were unable to determine the upper bound for distortions of this structure [Conway, J. H., & Torquato S. 2006, "PNAS" 103, 10612-10617] . Because this current optimum packing of tetrahedra is less than that of spheres, they suggest that the regular tetrahedra may be a counterexample to Ulam's conjecture that the optimal density for packing congruent spheres is smaller than that for any other convex body.


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