I finally got my own copy of Fowler and Manolopoulos's "An Atlas of Fullerenes" from the MIT coop at Kendall square last weekend. In the appendix of this book, there is a complete list of spiral codes for fullerenes with less or equal than 100 carbon atoms. So one can simply follow the spiral code to create the physical model of corresponding fullerene. More importantly, if we followed the simple weaving rule, no other information except the spiral code is required to make the correct physical model!
I made the only isomer of C72 and C74, which satisfies the IPR (isolated-pentagon rule) requirement, based on the spiral codes listed in the appendix immediately when I was back to Taiwan yesterday. Just as expected, the bead model of C72 has D6d symmetry, and the bead model of C74 has D3h symmetry as shown in the book.
C72: 1 7 9 11 13 18 22 24 27 34 36 38
C74: 1 7 9 11 14 23 26 28 30 32 35 38