The face-turning octahedron, whose simplest example is the Diamond Skewb, has the interesting feature that the face overhangs the plane that turns, allowing more leverage and possibly a better grip. Does this allow nice finger tricks?
The cubical Skewb and the concave Rubik's cube also have this feature. In contrast, in the Megaminx the turning face slants inward so it is harder to get a grip on it, inspiring innovative features like ridges.
Assuming one wanted to remove this feature (as an exercise in geometry) from the Skewb and Diamond Skewb and have the cutting planes be precisely orthogonal to where they meet the faces (like a Rubik's cube), what should be the shape of the polyhedron? (Because it is deep cut, a sphere would also work, but that is boring.) Answer might be the regular or rhombic dodecahedral shape mods of the Skewb.
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