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Tetrahedron Circumscribing


The (not necessarily regular) tetrahedron of least volume circumscribed around a convex body B with volume V is not known. If B 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.


See also

Triangle Circumscribing

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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 Circumscribing

Cite this as:

Weisstein, Eric W. "Tetrahedron Circumscribing." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TetrahedronCircumscribing.html

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