Assume my 3D model is a pyramid with a rectangular base and I numerate four corners of the base with 1, 2, 3, 4 and give 5 to the top point. If I project this pyramid into a 2D star-shaped object, would not all four outer points of the star be associated with the point number 5 in the 3D model? 
Does UV-mapping generate for some points of the 3D model several points in the 2D projection?
uv mapping