New Ideas For The Tangram Cube

This time when I got to the long edges it occurred to me that to flip two of them it would be an easy thing to flip one of them, move the other to the same edge, flip it, then move the slice wherever it needs to go. If I got good at it I could even do it before moving the slice home in the first place, so that at most to solve the long edges it would take a max of 4 moves if they are permuted already, but if they are not then it should only take 3 moves. Namely flip the one that is not home, move the other home, flip it. See? If you don’t get it, here is an example:

Say the blue orange and the green yellow need to flip, and the blue orange is where the green yellow edge needs to be. Flip the blue orange, replace with the green yellow, flip the green yellow. That’s it. Orienting and permuting all at once.

The other new idea is to solve some of the centers while you are orienting little edges, if possible.

New Improved Strategy

1. Solve the two little corners. 1 twist max.
2. Solve the six big corners. Use Edge Flips, Up Replace Down, and The Move. 
3. Solve the three long edges, if necessary. If they are already permuted, but two need to flip, flip one, replace it with the other, flip it and move it back. If they are not yet permuted, flip-move-flip, in such a way that they end up in the correct places.
4. Permute the three little edges using The Move.
5. Orient the three little edges using (LAR)x2. This flips the edges at the top left and the back right. It also does a double swap of centers that are adjacent to said edges, so this could be used to solve some of the centers as you are orienting little edges.
6. Solve the remaining centers. (JAJ’A)x3 (WLW’L)x3 is a 3-cycle from Bottom to Back to Right. W’RW swaps Bottom and Right, so doing it before the 3-cycle let’s you go from Bottom to Right to Back.