On Tetrahedral Containers

As has been noted here, the question of the smallest area isosceles triangle containing a given general triangle has been settled (https://arxiv.org/abs/2001.09525) and the smallest perimeter isosceles triangle container of a triangle also is pretty much done.

So, let me simply record here the question of raising this question to 3d - to contain a general tetrahedron with the smallest possible regular tetrahedron (will the side of the container be the same as the longest edge of the given general tet?) and many other possibilities...