Up to now, I guess that Chuang has constructed 11 high-genus fullerenes. The following figure shows eight of them. I have given high-genus dodecahedrons (d), (e), and (f) away as gifts, though. All five high-genus dodecahedrons in the figure are different in the sense that they have completely different arrangement of heptagons.
(a) High-genus tetrahedron.
(b) High-genus cube.
(c) (d) (e) (f) (g) High-genus dodecahedron.
(h) High-genus icosahedron.
I don't have beaded model for high-genus octahedron. Maybe I will construct one when I have time.