There's an issue with the larger part - there are slight overlaps and seams, which are basically invisible at normal zoom levels, but not to the path union algorithm, so it's not so straightforward. I'll post a step-by-step on youtube + pics, so it's clear what I'm talking about.
I'll add the outline mode anyway, if you have thousands of triangles in the unfolded parts, it can take considerable time to merge them.
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