Volumes of Similar Tetrahedra are in Triplicate Ratio of Corresponding Sides/Porism

Proof
Let them be divided into the tetrahedra, by virtue of the fact that the polygons forming their bases can be divided into triangles.

It follows from :
 * the triangles forming the bases of these tetrahedra are similar.

So from :
 * the ratio of one tetrahedron in the one complete pyramid to the corresponding tetrahedron in the other complete pyramid, so is the ratio of all the tetrahedra together in the one complete pyramid to all the tetrahedra together in the other complete pyramid.

But from :
 * the ratio of one tetrahedron to another tetrahedron is in triplicate ratio to their edges.

Hence the result.