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# Slicing up n-d shapes.

## Question

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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a rectangle

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a rectangle

If the cube was laying flat you would be right. But hanging it by a vertex causes a different shape.

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If the cube was laying flat you would be right. But hanging it by a vertex causes a different shape.

Aha, I answered for hanging by an edge and not vertex.

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a hexagon.

Can you hang a 4-d object in 3-d space?

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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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Presume the same action were possible

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