In August 2017 I bought a twisty puzzle—the Tangram Cube. I made several posts telling about solving it. The solution guide I presented. Recently, after a break from twisty puzzles for months, I started solving the puzzles in the case that were scrambled. Eventually I came across the Tangram Cube. I didn't even remember its name, let alone how to solve it. But I finally found my notes from 2017 in this blog, and was able to solve it. I've looked for a better way, a way in which I could easily solve the triangles (centers) near the beginning, and then use pure 3-cycles to solve other pieces, but I couldn't come up with anything. So here I present my current solution for the Tangram Cube.
Step 1. Solve the two little corners using at most one simple twist of W.
Step 2. Solve the six big corners 1 or more at a time by twisting edges or using Up Replace Down to get as many of them as possible then The Move to finish up. Use one of the Little Corners and one of the Edge turns with The Move.
Step 3. Solve the 3 long edges by moving the slice so they are in the correct spots, then if necessary flip two of them. Slide one to A, flip it, slide the other to A, flip it, slide if necessary. For example: K A K' A flips L and A. K A K A K flips L and R. Or you could use L or R as the flip spot and always only use 4 moves. If you need a pure flipper use (K A K' A) x 3 to flip L and A.
Step 4. Permute the 3 little edges using The Move with two Edges. (J A J' R) x 2 is a pure 3-cycle K1 to DE to YP.
Step 5. Orient the 3 little edges. (L A R) x 2 flips DE and YP. (J A J' R) x 2 (A K A K') x 2 is a pure flipper of K1 and YP.
Step 6. Solve the centers 1 or more at a time using (J A J' A) x 3 (W L W' L) x 3 which cycles Bottom > Back > Right. The setup move W' R W swaps the centers on the right and back so the cycle is reversed.
(J A J' A) x 3 is a 5-cycle. Right to Front to Left to Top to Back.
If the 3-cycle is only going to solve one piece why not solve one piece using the shorter 5-cycle instead?
Now that I have re-figured out the puzzle, it is time to have some fun with it for a while before moving on to other scrambled puzzles in the cabinet. :)
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