Trying to joint sketches/plates at an angle

[jchanXS2S2]

I have been trying to build a geodesic dome from polygons similar to a soccer ball, and fuse them together into one component to 3d print.  H used an online calculator to find the angles needed for the shapes, but it did not give the angles between the polygons/faces.  I was wondering if there is a way similar to sketches to set a "constraint" in an assembly between edges so it is free to rotate so I can constraint the other edges of the polygon to form the dome before joining the overlapping parts of the plates.

[jhackney1972]

With the proper polygons, the assembly will develop itself due to the fact adjacent joints must align to existing edges.  Maybe the attached model will give you a hint.  In the model I have move the Timeline marker to the left two places to remove the smooth exterior of the ball to show the polygon segments.