Is it possible to have self intersecting polygons in shapefile?

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GIS vector data for example shapefile contains polygonal data.

Lets assume, we have polygon A which has self-intersection which means that the edges in this polygon intersect with each other.

Lets say if we want to intersect A with polygon B, then the steps of computing the overlaid polygon differs whether A is a polygon with self-intersections or not.

Do the polygons in one map layer have self-intersections or not?

I searched for this question on internet and I found couple of instances where people complain about error caused while importing data due to the presence of self-intersecting polygons.

Also I got the impression that self intersecting polygons are not possible in certain file formats.



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