I'm interested in finding algorithms to do a superflip on a megaminx -- that is, to rotate all 30 edge pieces by 180 degrees around a central axis. In particular, I'm interested in approximating the smallest possible length of a superflip. This is a hard number to calculate and is related to God's number for the megaminx. (God's number for the rubicube is 20, and a rubik's superflip takes 20 moves.) Here's what I know so far:

1. A megaminx superflip takes at least 24 moves. Proof: Consider the "join" between a corner piece and a neighbouring edge piece. There are three of these for each corner piece. Each corner piece must leave an edge piece and then come back to it flipped. It can't do this in one move, so it must move twice with respect to that join. That makes a total of 20*3*2 = 120 join changes. Each face move changes 5 joins, so a superflip requires at least 120/5 = 24 moves. (Can a similar proof technique yield a better limit, like 36 or 48?)

2. A superflip can be done in 83 moves. Here are the moves:
[6]'[9]'[4][11] ([1][2]'[1][2]2[3]'2)*6 [11]'[4]'[9][6] ([12]'2[9][11]'[7]'[8]')*9
(Number a face [1], then number touching faces [2] to [6] in clockwise order, then number [7] opposite [2], [8] opposite [3] etc, and finally [12] opposite [1] -- sorry if there's already a standard notation for the whole megaminx but I couldn't find one.)
I found this one by doing a lot of computer searching.

So an optimal superflip takes N moves, and 24 <= N <= 83. I'd be interested to hear if either of these limits can be improved upon... More generally, it would be interesting if there was *any* pattern on the megaminx for which tighter limits than 24,83 could be found.

The upper limit seems very high. All you need to do is find a shorter path than 83 moves. I'm sure someone on this forum (or perhaps the speedsolving forum) can provide an algorithm to beat this limit. Anyone?

Maybe mention this in the patterns thread?