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What is the maximum number of vertices for polygons and polylines (including multipart) in PostGIS?

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I believe it is a setting somewhere, Oracle spatial I think has a limit of 8999. –  Brad Nesom Apr 26 '13 at 18:30
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The only link I could find about this is a post on the discussion group tittled, What is maximum limit(max number of coordinates) for a LineString? where it is mentioned that

It's a 32bit integer, so theoretically you should be able to have up to 4,294,967,295 vertices per line.

I would believe that the same limit would hold for a polygon.

Your question however raises more questions. What exactly are you trying to do where you would be concerned about the limit of vertices in a polygon? If you are indeed running into this limit, then you are definitely doing something wrong.

Update According to this comment by Paul Ramsey, the Number of vertices is lower:

This is correct, though the npoints counter is a signed integer (oh well), so you can "only" get 2 billion vertices in.

So there you have the answer straight from the horse's (elephant's ?) mouth.

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This is correct, though the npoints counter is a signed integer (oh well), so you can "only" get 2 billion vertices in. –  Paul Ramsey May 1 '13 at 0:06
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