The QiYi Fisher Cube is the classic shape modification and still one of the best. It is a 3×3 with the cutting planes rotated 45 degrees, so the edges become corners and the whole puzzle changes shape as you scramble it.
It solves with the same method as a 3×3, with two complications. You are solving by shape as much as by colour, because the pieces no longer sit where you expect. And it can reach an apparent parity, where a single edge looks flipped, which cannot happen on an ordinary cube and catches people out the first time.
The QiYi Fisher Cube turns quickly and corner cuts well, which is not a given on shape mods. Plenty of them are handsome and unusable.
It suits someone who solves a 3×3 comfortably and would like their assumptions disturbed.

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