Here's a couple of not-quite near misses I created recently. They're like near misses, but maybe not quite close enough to earn the title. They're interesting though for the polygons they involve.
First one has regular enneagonal faces (9-gons).
Stel file: http://www.software3d.com/StelFiles/Ico ... agons.stel
Second one has regular pentadecagonal faces (15-gons).
Stel file: http://www.software3d.com/StelFiles/Ico ... agons.stel