Graphs and Solutions Representation

I have found a little more than fifty solutions from three of the nineteen beginning positions of the yellow "Tee" and violet "Crystal" pieces I am proposing will root two hundred forty unique solutions.   Originally I had  conceived of recording all of the solutions on paper and colored pencil then cutting up the solutions and arranging them on a wall to create a tree graph representation that would grow as I found more solutions.  Alas I do not have a big enough wall.

The figure below shows a previous tree graph made using yEd graph editor:
https://www.yworks.com/products/yed

This tree graph if printed out with a 12 point font is about 8 feet x 8 feet.  It certainly has the potential to be a very beautiful representation but I haven't figured out how to get the node colors yet.

The solutions used in this instance were from and existing set from a paper by Peter Orth that provided a table of all the solutions normalized to the Tee on the front edge:
http://www.sciencedirect.com/science/article/pii/0012365X85901608

I have settled on recording the solutions directly into a spreadsheet page that translates the entered solutions on a cube grid into formats compatible to yEd.

This is what I have so far.  It looks interesting and might be understood by someone particularly if there were lots of Soma puzzles laying around near the graphs.  It would fit on an 11x17 sheet size.  The next tree will be more challenging as it has thirty two solutions