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Suppose the top face of the pyramid is ABCD with the square EFGH directly below it.

Suppose AC and BD meet at P, the apex of the pyramid.

Make a cut with a plane through P which is parallel to AB and goes through EF.

Make a cut with a plane through P which is parallel to BC and goes through FG.

Make a cut with a plane through P which is parallel to CD and goes through GH.

Make a cut with a plane through P which is parallel to DA and goes through HE.


The result will be the square-based pyramid PEFGH.


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