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I have a set of polygons and I want to find minimal distances between the edge of each pair of them.

It's a similar task to Finding minimum edge to edge distance of polygons using ArcMap but how do I do it in SpatiaLite?

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The ST_Distance function in the link you referenced works the same in SpatiaLite. You can import your polygons into SpatiaLite and calculate min distances there.

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