Snapping vertices in a particle system The idea is to snap the four (selected) polar vertices to each other while scaling the particle (meeting snap point, in this case, is the coordinate center). Eventually I'd like to make the sphere radius equal to the length of the tetrahedron edge in such a way to align the vertex grids so that boolean operations can be implemented. 
Can it be done this way or is there a better alternative ? 

Basically in order to make this 


Boolean didn't turn out well in the depicted orientation of the spheres, even though the vertices appeared to be aligning.
With some inspiration from this answered question, though some settings must have been changed because I can't find the other size determining value, he pointed out, I managed to find the right Render>size "0.25" which makes the particles the same size as the original Dupli Object and takes the selected polar vertices to the same spot as I wanted. 

and to do the eventual How to convert particles to mesh? 
and How to Make Multi User Objects Single User?
is required