Comments on type-II high-genus fullerenes

It is of interest to compare the bead model of a dodecahedron fused by 20 C60 in the previous post to high-genus fullerenes we discussed before. In fact, one can also view that bead model as a high-genus fullerene with genus=11, which is obtained by substracting one from the number of faces in a dodecahedron. The most important difference between these two types of high-genus fullerenes is the orientations of the TCNT necks relative the surface of the polyhedron. In the original high-genus fullerenes, which I will call the type-I high-genus fullerene from now on, the orientations of the TCNT necks are along the normal of the polyhedron. Here in the type-II high-genus fullerene, the orientations of the TCNT necks, which are created by fusing two neighbored C60, are lying on the surface of polyhedron (dodecahedron here) and along the directions of its edges.