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four UV sphere tetrahedral particle system, central polar vertex alignment snap

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 enter image description here

Boolean didn't turn out well in the depicted orientation of the spheres, even though the vertices appeared to be aligning.

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    $\begingroup$ Not sure to get the point. You want to merge the 4 spheres in order to obtain the figure that is rotating? What's the link with particles? $\endgroup$ – lemon Jul 10 '19 at 12:12
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    $\begingroup$ Knowing what I know now, I realize the spheres could be positioned individually. Also the dupli objects (spheres) can probably be made "real" and THEN positioned individually. So really I'm asking you, how would you do it ? Or more generally, how would you make a sphere grid, that can be subjected to boolean operations, because verices are aligned to allow that ? $\endgroup$ – t8ja Jul 11 '19 at 16:06
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    $\begingroup$ is that of some help? i.stack.imgur.com/gPKgM.gif $\endgroup$ – lemon Jul 11 '19 at 16:13
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    $\begingroup$ ok, I get it now. Leander has done it here blender.stackexchange.com/questions/136607/…. Keyword was Reuleaux! $\endgroup$ – lemon Jul 11 '19 at 16:25
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    $\begingroup$ simply a shape key from a subdivided tetrahedron and itself turned into a sphere. $\endgroup$ – lemon Jul 11 '19 at 16:35
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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. result

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

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