Tetrahedron Circumscribing

The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body  with volume  is not known. If  is a parallelepiped, then the smallest-volume tetrahedron containing it has volume 9/2. It is conjectured that this is the worst possible fit for the general problem, but this remains unproved.

REFERENCES:

Finch, S. R. "Geometric Probability Constants." §8.1 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 479-484, 2003.

van der Burg, J. W. "An Accurate and Robust Algorithm for the In-Sphere Criterion for Automated Delaunay-Based Tetrahedral Grid Generation." Paper P 98212 presented at The 6th International Conference on Numerical Grid Generation for Computational Field Simulation, University of Greenwich, London, July 1998. 1998.