Slicing a cube to get a hexagon

Question

Slice through a solid cube with one flat cut (a plane). Depending on the angle, the exposed cross-section can be a triangle, a rectangle, a square, or other shapes.

Can a single straight cut through a cube produce a perfect regular hexagon? If so, where do you cut?

Accepted Answer

Yes, a cube has a regular hexagonal cross-section, and it appears when you cut perpendicular to a space diagonal, through the cube's center. Set up the cut. A cube has four "space diagonals" running from a corner through the center to the opposite corner. Pick one such diagonal. Now slice with the plane that passes through the center of the cube and is perpendicular to that diagonal. Why the cross-section has six sides. This slicing plane cuts across six of the cube's twelve edges, it slices through the midpoint of six edges, missing the two corners that lie on the chosen diagonal (and the ed…

Slicing a cube to get a hexagon

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