I haven’t encountered many polyhedra which feature regular pentadecagons, and geometry textbooks generally don’t even use that word, calling them “15-gons,” instead. The pentadecagon happens to be one of my favorite polygons, though, and has been ever since I independently figured out, a few years back, how to duplicate the ancient Greeks’ accomplishment of combining the Euclidean constructions for the regular pentagon and equilateral triangle, in order to construct a regular pentadecagon.

The one above also includes regular decagons as faces — but I had to let the pentadecagons intersect each other to get that to work.

This third polyhedron resembles a truncated icosahedron, but with pentadecagons replacing that solid’s twenty hexagons. The pentagons are still in place, with two types of trapezoid and some very thin rectangles needed to fill the gaps.

These images were all created using Stella 4d, software you may try or buy at http://www.software3d.com/Stella.php.