This might not be what your idea is originally, but here's images for your text-only explanations. Instead of the user inputting the number of possible snappings, i.e. using 360/n , I'd prefer just a button toggling between snap with 360/12 degrees and no snap. 12 is for the number of those gaps on the port, which look like where latches can extrude out of them to grab onto another port. The rest of the possible snapping positions can be adjusted with the new gizmo.