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I recently got started using GAP, and wrote a C++ program that generates legal scrambles in cyclic-notation for GAP, and some GAP code that gives solutions to them using the "PreimageRepresentative" function. On short scrmables, it can produce the reverse turns to solve it (likely optimal). But for a random scramble of say 500 turns it produces solutions over 14000 turns (in the analog of QTM or 'word-length' in the freegroup). This is not satisfactory to me because I can solve it by hand using less than 1000 turns doing centers-first.



You can play with this puzzle here (it doesn't physically exist yet):
http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/dodeca_f6.htm