This puzzle is kicking my ass. Fortunately, our hero Super Antonio Vivaldi made a tutorial (including another video with algorithms and another on the regular Icosamate.)
Step One: Get Corners On One Face
This should be done intuitively. Use a beginner’s method to move/rotate these as you go on.
Step Two: Permute Last-Layer Corners
This is a challenge and will be the most time-consuming part of your solve. First, flip the puzzle over and remember your bottom-layer colors (it’s easy to get mixed up and forget, particularly after putting the puzzle down!) Now, you’re going to find one corner to use as a basis for figuring out what the top piece must be.
You will do a DDUU algorithm as expected. This swaps the top with the front center piece and it also swaps the back left and back right. Doing the algorithm a second time returns all to their proper spots. However, it will also rotate them.
Starting on the left side, this will spin those centers clockwise. Counter-clockwise is done starting on the right.
Usually you won’t have this all land perfectly. Remember some cheats: you can move up the front L & R pieces to the back L & R. Since those back ones will swap/rotate and the front won’t, it’s an easy way to move around which pieces you want.
If you’re stuck with a pair of adjacent ones, do the algorithm once. This swaps the top and the center. Then rotate the second wrong piece to the front and do the alg again. This is how you do a three-cycle. Make sure you do the DDUU on the right to start and then return with the left to ensure the back sides don’t get messed up.
Step Three: Rotate Last-Layer Corners
Get the top center rotated properly while keeping at least one corner oriented properly. You’ll do your DDUU until the top center is right (and you keep one aligned perfectly so you know which is which).
Now you’re going to get the remaining corners. You can have two or three out – never one. This is a beginner’s method approach using R’/D’/R/D. You’ll count how many turns you need. You will be looking for a multiple of five (to keep your top oriented correctly). You do your R’/D’/R/D until one corner is set. Then, using a last-layer method from a 3×3, keep the lower-right piece in place (it’s rotated wrong now). Keep doing the algorithm a total of five times (or multiple of five). If it’s not a multiple of five, that’s OK, now use the one incorrectly-rotated center as your center.
If you’re unlucky and get parity, you’ll find yourself with everything done and an incorrectly-oriented top center as stated above. In order to fix this, place your top center how it’s supposed to be. This will mess with the other five corners. *sigh*. Yup. Now using intuition, move around these pieces to get the top layer perfect.
I’m guessing here, but you’ll likely swap a top and a front – then turn the puzzle and perform the opposite algorithm (starting on left vs right). You’ll likely need to fix the piece you just put in place. Feel free to do so (clockwise or ccw).
If you get all those pieces put in properly, you’ll likely have a few corners which need rotations. Count how many you need: hopefully you’ll end up with five rotations and go back to the R’/D’/R/D to figure it all out.
Step Four: Match Edges
This three-cycle will swap edges. This will go red/green/blue clockwise if you start on the right. Like the Face Turning Octahedron algorithm, this will require you to bring one slice down, then do a D/D/U – return slice – D/U/U algorithm.
Starting on the left will rotate them clockwise (R/G/B). You will use a face with a V in front of you (like the blue/green shown here). If you bring the left (red) piece down, then you do Right down, left down, right up – return slice – right down, left up, right up.
If you start on the right (move yellow down to the blue), then your algorithm will go left down, right down, left up – return slice – left down, right up, left up.
Now…what to do when a pair are inevitably flipped upside down? OK, so get them adjacent like you’ve been doing. You’ll be flipping these, so hopefully these are your last two edges that need fixing. If they’re the blue and green here, use a dummy piece (yellow) as a start. Now, you’re going to want to flip the green piece. Do this by the following:
You’re going to be working with the lower-right corner (LR – the green triangle) and bottom layer. Turn LR’, then D, D, and return LR LR. This will flip the piece that was originally there.
Now, do your algorithm. Then undo your flip, now by LR’, LR’ D’, D’ and LR – the opposite of your prior flipping alg. Finally, do your step-four algorithm two more times. If you need guidance, check out SAV’s tutorial (with timestamp).
Step Five: Match Petals
This algorithm is the opposite of the step-four alg. Here, however, you will move up the M slice layer, perform three moves, return the M slice and then do three more. It’s almost exactly the opposite of the one above. I need time to get to this part.
Start by moving that M slice up to put the pink petal where the yellow is. Then, using the colored center as your basis, do a Right down (x2), left down (x2), right up (x2) then restore the M slice to its original spot and do a Right down (x2), left up (x2), right up (x2).
Update: A solid week of dedicated work resulted in a full solve. One of my proudest solves. Not sure how eager I am to mix this up again. :D
