not sure I have understood the problem correctly… what I got is to identify which triangle belongs to which facet, considering that for a triangle to belong to a facet its longest bottom-edge should lie on the facet itself (so we can just plainly ignore its shortest in case a triangle has more than one bottom edge)
if that is right, I would do something like this, I believe the only external component is create tree from elefront… but anything that creates branches based on a list of integers to indicate which branch the items should be assigned to should work?
buckypuzzle_Re.gh (235.0 KB)
it measures the closest distance-point between the center point of the longest bottom-edge of each triangle, and each facet, so for each triangle you get a list of distances among which only ones says 0 (well… it says “very little” 
)
then with item index you retrieve the index of that distance (which is equal to the index of the facet it belongs to) and assign each triangle to that branch