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A two layer (per)face turning Dürer's Solid.
This puzzle is not the first to use that shape, in fact, it is the second, but this is the first that is not a shape-mod.
The reason why the professor version was created before a standard one is because all of the previous puzzles of the inventor (James) were order 1 (one layer), and he wanted to create a higher order puzzle.
His (understandable) decision has improved the puzzle unexpectedly, because of the extra layer, the inner layers are less bandaged and it allow more scrambling.
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Thank you to the following people for their assistance in helping collect the information on this page: polymaker.
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