i dont quite understand what you mean by 'have an edge going through the middle?'
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Basically, you don't want to cut out a hole in the center of a face. You want the hole to be touching an edge. For example, if you wanted to use boolean difference to cut out a hole in the center of a face, you need to put an edge going through the center of the face first. That way, after you cut out the hole, the hole is connected to the rest of the geometry with an edge (it's not a floating hole, which will cause major problems with the geo).
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