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Slicing up n-d shapes.



Hang a cube from one of its vertices. Now, if you slice it horizontally through its center, what 2-d shape will the slice yield?
What if you do this with a 4-dimensional cube, i.e., a tesseract? The slice will yield a 3-dimensional object--- what does it look like?
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Hexagon - Hanging it from one vertices will cause another to be at the very bottom. The remaining six vertices will be equidistant from a horizontal plane cut through the center, three above and three below. All six sides of the cube will pass through the horizontal plane, each with the same percentage of their area above or below the plane. (Three will be reversed from the other three) The shape created on the horizontal plane will have six sides with equal length and equal angles between then - Hexagon

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