Intersect Faces Issue

It’s because of the small size of your model. SketchUp won’t create the required tiny faces. They can exist but you have to create them at a larger size.

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That gap is about the width of a human hair. Other gaps are smaller. I think you’re cat head is excessively over modeled.

Try scaling it up by a factor of 100 or 1000. Or use The Dave Method.

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