This symmetrohedron has the twelve regular decagons, twenty regular hexagons, and thirty squares of its “parent,” the great rhombicosidodecahedron. It was modified by using the “morph duals at 50% by tilting to rectify” function, twice. This left the resulting polyhedron with additional faces: 180 trapezoids (60 each, of three types), and 120 scalene triangles. That’s 362 faces in all. I made it using Stella 4d, which you can try for yourself, free, at http://www.software3d.com/Stella.php.