A cube is sliced into halves in such a way that cut is a regular hexagon. What is angle between plane of cut and base?

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A cube is sliced into halves in such a way that the cut is a regular hexagon. What is the angle (in degrees) between the plane of the cut and the base of the cube?

Visualize a cube. You know it has 6 faces, 8 corners, and 12 edges. Now, imagine a knife slicing away each corner with a straight plane cut. How many total edges are there now?