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.
Tetrahedron Circumscribing
See also
Triangle CircumscribingExplore with Wolfram|Alpha
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.Referenced on Wolfram|Alpha
Tetrahedron CircumscribingCite this as:
Weisstein, Eric W. "Tetrahedron Circumscribing." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TetrahedronCircumscribing.html