@Zakara I wouldn't fret, those tri's are peanuts, and are crucial to have that sort of result, as it wouldn't come out as well if the carpet was just 1 polygon plane.
Thanks for the suggestions. I ended up just cutting the polygons to eliminate the overlaps. Works OK in most cases. A few dark corners remain here and there but whatever.
If you are working in maya (which it looks like) go under Create - polygon Primitives - Platonic Solids option box and choose Dodecahedron. No need to snap vertices=)
Delete the 2 polygons at the ends and then either move the two sets of 4 closer together and weld with the right threshhold or target weld them together one by one.
Question: are those merged into the same object or are they separate objects? I'm frankly amazed if you got that many polygons into a single batch without hitting big problems.