Notes1. Pure buckminsterfullerene forms a more disorderly hexagonal closest packing of molecules (hcp). Hexagonal packing, like face centered cubic packing, consists of layers of spheres sandwiched together, each layer appearing like pool balls in a triangular rack. In the facecentered arrangement, spheres are consistently located above the voids two levels below. Hexagonal packings do not follow this rule and are therefore more random. They have the same density, however.  
2. Assuming a soughtfor polynomial of the third degree N = AF^{3}+ BF^{2}+ CF + D, one may substitute corresponding values of F and N, e.g. the (F,N) pairs (1, 13), (2, 55), (3, 147) and (4, 309). The resulting set of four linear equations may then be solved to obtain the coefficients (A,B,C,D).  
4. An isomatrix of higher frequency will accommodate both the bcp and XYZ lattices.  
9. Synergetics is not designed to prohibit or preclude our use of XYZ reference frames, which may be modeled with their origins at the centers of 4D octahedra (octahedra may be developed from tetrahedra by truncation). We may also employ linear transformations for converting Cartesian cubes into rhombohedra and vice versa, rhombohedra being the "fundamental parallelotopes" of the fcc lattice, thereby allowing all integral coordinates (a,b,c) to attach to all the centers of closest packed spheres. Six prime vectors, and their six 180 degree counterparts, pointing from a sphere center to all 12 surrounding sphere centers, may then be defined using combinations of 1s and 0s for (a,b,c). Andrew Frank, a former BFI volunteer, supplied some of the insights leading to this construction.  
12. Barry Cipra, "Music of the Spheres," Science, Vol 251 pg. 1028.  
13. The vector equilibrium (VE) is actually formed by 8 edgebonded tetrahedra gathered around a common central vertex, which gives 24 radial vectors in addition to the 24 circumferential vectors.  
14. John Polkinghorne, Science and Creation (Boston: New Science Library, 1989), pp. 356.  
15. Rolf Landaur, "Wanted: a physically possible theory of physics," IEEE Spectrum, September, 1967, pg. 105.  
16. Elizabeth Corcoran, "Computing Reality," Scientific American, January, 1991, p. 107.  
17. The reason NASA would fund such a study is to better understand how structures might be folded into a payload and then unfolded in space  see 2:795.05.  
18. For a more comprehensive inventory of jitterbugstyle transformations and treatment of their computerization see: H.F. Verheyen, "The Complete Set of Jitterbug Transformations and the Analysis of their Motion," Computers Math. Applic. (Vol 17, No. 13, pp. 203250, 1989), reprints from Pergamon Press.  
19. E.J. Applewhite, Synergetics Dictionary (New York: Garland Publishing, Inc., 1986); Vol. 1, p. 326, cards 12 (Computer as Antibody).  
