To create a faceted icosidodecahedron, you simply start with an icosidodecahedron, then remove its edges and faces. Next, you connect the vertices differently, thus creating new faces and edges. As you can see below, this can be done in many different ways.

All these were created using Stella 4d, software you may try for free at http://www.software3d.com/Stella.php.