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My data consists of equal-sized polygons. I need to identify and select all the polygons that border two or more polygons.

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if they touch, you can always run the topology rule and check the output report (webhelp.esri.com/arcgisserver/9.3/java/index.htm#geodatabases/…) –  A.R Nov 27 '12 at 12:04
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If you have ArcGIS for Desktop then I think the Polygon Neighbors tool will provide access to those polygons which have two or more edge neighbors.

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