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Cutting rectangle set (not squares) into triangles using ArcGIS for Desktop?

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I have some large features that I need to split into smaller pieces for terrain alignment through vertices in another program. I figured triangles would be the best solution.

So basically I want to turn this:

enter image description here

into this:

enter image description here

Sadly the latter image is a mockup. I had some success with the fishnet tool and intersecting to create rectangles, but I can’t get triangles out of it. Rotating the net doesn’t work because the rectangles aren’t square. Any ideas that don’t involve manual cutting?


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