Generate aggregated surface from four different quadrillaterals which share two edges.

I am trying to generate a form using a set of four polygons only. These
polygons must remain rigid, so I am not looking to parametrically
stretch or rescale their properties along some existing surface. I just
need a script that will
automatically orient my four polygons  (in 3 dimensions) along edges
that they share (each shares at least 2 edges with the others). It
would be wonderful if this included the opportunity to adjust the
complexity
of the aggregation with some kind of slider.  Also helpful would be the
ability to "freeze"
certain aggregations that are interesting, while continuing to adjust
the connections which are not.

In can include pictures of the polygons if this is helpful. They are all cut from then same plane