Tetrahedron ellipsoids
Given an arbitrary tetrahedron, consider the maximum volume inscribed ellipsoid (i.e. ellipsoid inside it touching its four faces), and the minimum volume circumscribed ellipsoid (i.e. ellipsoid passing through its four vertices), then these two ellipsoids have the same center, and they are related by uniform scaling (i.e. the same scale in all directions) about that center.
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