Hi Cage,  Oh and belated Happy Birthday greetings ;-)

Yes I can understand that. So if a vertex was a corner of a dozen polygons, such as maybe the centre of a circle made of twelve segments, and for some reason the UV  mapping separated those dozen polygons onto different areas of the map, then that one vertex would have a dozen different but equally valid UV coordinates.

That is an interesting problem. I wish I was better at maths, and programming. I find puzzles like this fascinating.

Cheers

Ian