Let $A$ be a n-dimensional parallelotope and $v \in \mathbb{R}^n$ a vector. Is there a formula giving the volume of the symmetric difference $A \Delta (v+A)$?
2026-04-04 21:01:24.1775336484
Volume of the symmetric difference between a parallelotope and its translated.
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The overlap (if any) of the two versions of the parallelotope is again a parellelotope $B$, with the same face normals as $A$. The volume of the symmetric difference is just twice the difference of the volumes of $A$ and $B$. How to put that into a formula depends on how the parallelotope is given.