Cage, yes - correct on all counts.  The code is building lists of polygons that live in some particular region based on whether any vertices of a polygon reside there.  This does allow the polygons to be listed in more than one region.  The problem is that a polygon (say a triangle) vertices might live in region 0, 1 and 4 (assuming a division of 2, with regions numbered 0-7).  That polygon might well span across the corner of region 5, but it won;t end up in region 5's polygon list, since none of it's vertices live there.

The only way I see to fix this off-hand is to test the edges of the polygons, instead of the vertices.

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