I think the Tuttminx is a fun puzzle that offers plenty of variety during the solve. I've been working on algorithms and strategies and I can solve it reasonably well, though it currently takes a bit longer than I'd like!
I am interested in the last layer strategies of my fellow Tuttminx enthusiasts. In particular, how do you flip the last hexagon edges (or keep them from being flipped)? What face are you using as the topmost (hexagon or pentagon)?
I am using a pentagon for the topmost face because it simplifies the last layer to five hexagons. At first, I tried to approach the last layer like a gigaminx by solving all the surrounding hexagons except one. This was horrendous as I had to repeatedly break completed faces to flip hexagon edges. My current strategy works but still seems inefficient: I place all of the hexagon edges, which takes some wrangling as many of them reach the last layer flipped. Next, I insert the lower pentagon edges. Finally, I insert the corners below the upper pentagon (sixteen of them) using an algorithm that cycles corners from one pentagon to another. This all works, but it is a lot of turning compared to the edge assembly and insertion method that I use in the lower layers. I have enough algorithms that the final pentagon edges and corners are no more difficult than a megaminx.
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