Nest complementary objects quick, without having to deform,distort? These are just simple placeholders for any two complementary objects which would have many vertices placed in the same location.

To get this picture I had to distort the tetrahedron and pull each of its' vertices to the vertices of the cube, by moving the cursor from vertice to vertice, and go into Edit mode of the tetrahedron to actually move its' vertices one at a time.

Is it possible to achieve the same result without distortion along the way, and in less steps ? 

I already posed a similar question which was answered, but wasn't general enough, because the objects had a common axis, which made the alignment rely solely on Rotation... while simultaneous Scaling AND Rotation is required in most cases.
To construct the dual object, you can:


X Delete > 'Faces Only' of the original
F between selected vertices to create new edges
F selected edges to create new faces




If you already have the complementary objects, not in the right orientation or scale, maybe this answer will help?

EDIT: following commentary .. this sequence was keyed manually, forward and in reverse from a static exact fit position. I personally think 'cheating' is the easiest approach.