fanwuq
Legend
I've been working on an advanced pyraminx solution. I need some help to develop it.
Overview:
1.Extended “cross”-- orient the corners(not tips) to the same side while inserting the first edge of the first layer if you see it.
2.insert last 2 first layer edges with one alg, possibly with a commutator, at the same time.
3.Solve with one look LL.
Tips can be corrected anytime.
Advantages to this method:
Easy to learn, not too many algs, very fast with practice, cases are fairly easy to recognize, less moves than all methods that I know of except possibly Michael Gottlieb's “ZBLL pyraminx solution” with 90+ algs.
First step is obvious and intuitional. Rather than just doing the “cross,” it would save a few moves by inserting one edge at the same time if you can see it during preinspection. (I can't always.) Also, if you immediately see a better face to solve, you can do it. (should be no more than 5 moves, excluding correcting tips which I also do at this step.)
2.This step need to be developed. I can already see that some difficult cases for solving the last 2 edges only can be solved faster by doing one of the LL algs. It should be possible to setup to any LL case in a move or 2 and do that, but I don't know if that is better on many cases than pure intuition. Optimal algs are needed. Perhaps you can orient edges at this step to do only sunes to finish LL. Lots of possibilities here. There are many 3 cycle commutator on this puzzle. Some of should help at this step. (Should be less than 8 moves with method complete.)
3.Everyone already do this anyway, i think. (7 moves excluding AUF)
So overall, I would estimate the average number of moves to solve is 17 with this method as opposed to about 26 with my current method which is intuitive First layer, much like the first layer of beginers LBL for 3x3.
Overview:
1.Extended “cross”-- orient the corners(not tips) to the same side while inserting the first edge of the first layer if you see it.
2.insert last 2 first layer edges with one alg, possibly with a commutator, at the same time.
3.Solve with one look LL.
Tips can be corrected anytime.
Advantages to this method:
Easy to learn, not too many algs, very fast with practice, cases are fairly easy to recognize, less moves than all methods that I know of except possibly Michael Gottlieb's “ZBLL pyraminx solution” with 90+ algs.
First step is obvious and intuitional. Rather than just doing the “cross,” it would save a few moves by inserting one edge at the same time if you can see it during preinspection. (I can't always.) Also, if you immediately see a better face to solve, you can do it. (should be no more than 5 moves, excluding correcting tips which I also do at this step.)
2.This step need to be developed. I can already see that some difficult cases for solving the last 2 edges only can be solved faster by doing one of the LL algs. It should be possible to setup to any LL case in a move or 2 and do that, but I don't know if that is better on many cases than pure intuition. Optimal algs are needed. Perhaps you can orient edges at this step to do only sunes to finish LL. Lots of possibilities here. There are many 3 cycle commutator on this puzzle. Some of should help at this step. (Should be less than 8 moves with method complete.)
3.Everyone already do this anyway, i think. (7 moves excluding AUF)
So overall, I would estimate the average number of moves to solve is 17 with this method as opposed to about 26 with my current method which is intuitive First layer, much like the first layer of beginers LBL for 3x3.
Except I usually do the tips earlier, to take advantage of otherwise wasted delays on my part.
I like your idea, though, it could be very fast. Maybe you could also solve the last five edges a bit more Heise-style: solve one edge in the first layer and one in the last, and then the last three in one step (which has a lot of 4-move algs as ooveehoo pointed out).
But I came up with a new method for it. It's only 2 looks. One look during pre-inspection, and only one look during solving. 
