I'm really liking the idea of doing megaminx orient-permute, for both corners and edges. Of course, you have to sort of arbitrarily pick a "correct" orientation; it doesn't matter what it is; it just has to be fixed. At first, it sounds like a really stupid idea, but there are two big advantages:
1. For permutation, you only need 30 "letters" for the edges, and 20 letters for the corners, so it's much more manageable - you can just use the same memo scheme you use for normal cubes, but with 6 extra letters worth of pairs for the edges. I think it will make memo much more manageable.
2. When it comes to solving, you'll have fewer cases to deal with setting up for the next algorithm, since the pieces are already oriented a certain way.
When I've done megaminx BLD in the past, I assigned each face a letter (A-L), and then assigned each sticker on that face a letter (A-E). Then I did face-sticker as a letter pair. So I needed a full letter pair for each piece. So by going to orient-permute, I'll be able to pack permutation two to an image. Orientation I could pack even tighter (perhaps hexadecimal, like I once did years ago for cubes). So the memo should actually be smaller with orient-permute, and hopefully it will be less confusing to encode, decode, and solve.
But I still haven't gotten around to trying orient-permute yet; maybe it won't work well at all. I'm looking forward to finding out. I will probably try it sometime early next year. (For now, I'm still trying to get through the Christmas Competition.
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