To create this, I augmented the red pentadecagons in the polyhedron found on the last post with antiprisms, augmented the slightly larger green pentadecagons with prisms, and then took the convex hull of the result. I like this one better than the last one, on purely aesthetic grounds.

Software credit: I used Stella 4d to make this, which is available at http://www.software3d.com/Stella.php.