High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! 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 regular tetrahedron. Currently, the best lower bound achieved on the optimal packing fraction of regular tetrahedra is 85.63%. It is known that the tetrahedron does not tile space, and thus its optimal packing fraction is under 100%, but no lower upper bound has been rigorously shown.

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