It looks like a Rubik's Cube and it turns like a Rubik's Cube, but what is it? Of course, it is a Rubik's Cube. HandiCube was suggested by Jens Renders. The regular Rubik's Cube is impractical to solve one-handed, as the solver would need to block two layers to make a slice move (middle-layer "M-turn"). This problem is solved in HandiCube by building the puzzles from a 2x2x2 cube, and having the edges and centers hang between the corners.
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directly if you are interested in obtaining a fully colored, stickered and assembled sample of this puzzle.