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Maybe this would work. Remove the stone halves from the base. Rotate each half 180 degrees and bring the square ends together. You should have two square ends that match up and the original bottom...

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Use a combination carpenter's square. Then just cut on the pencil line. Draw a center line and a cross line. Then saw carefully.

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You should be able to accomplish that with a hack saw. Either 24 tpi or 32 tpi. Let us know how you make out.