GEODESIC DOMES AND FULLERENES

The structural form of geodesic domes, composed of pentagons and hexag ons, played an important role in understanding the structure of carbon clusters. In this paper an analogy between geodesic domes and fullere nes is investigated. A brief survey is given of the geometry of geodes ic domes applied in engineering practice, in particular of the geodesi c domes bounded by pentagons and hexagons. A connection is also made b etween these sorts of geodesic domes and the mathematical problem of t he determination of the smallest diameter of n equal circles by which the surface of a sphere can be covered without gaps. It is shown that the conjectured solutions to the sphere-covering problem provide topol ogically the same configurations as fullerene polyhedra for some value s of n. Mechanical models of fullerenes, composed of equal rigid nodes and equal elastic bars are also investigated, and the equilibrium sha pes of the space frames that model C28, C60 and C240 are presented.