Geometrical Analysis of Radiolaria and Fullerene Structures: Who Gets the Credit? Academic Article uri icon


  • Marjorie Senechal. T he 1985 discovery of the C60 molecule, with carbon atoms at the 60 vertices of a truncated icosahedron (Fig. 1), by Harold W. Kroto, Richard E. Smalley, Robert F. Curl, and coauthors [1] was an important event in the nanotechnology revolution. The discoverers named it buckminsterfullerene, after the American architect Buckminster Fuller. The now-famous family of fullerenes—molecules of pure carbon in the shape of convex polyhedra with degree-3 vertices and pentagonal and hexagonal faces—soon followed [2]. For any convex polyhedron with F faces, E edges, and V vertices, we have the Euler relation V – E + F = 2. It is easy to show that the faces cannot all be hexagons. For fullerenes, where f6 and f5 are the numbers of hexagonal and pentagonal faces, respectively, it is almost as easy to show that f5 = 12and V = 2(10 + f6). Thus the number of pentagonal faces is always 12. The value of f6 can be any number but 1 [3]. Accordingly, the smallest fullerene, C20, has a shape of the dodecahedron, formed only by pentagons. The next fullerenes are C24, C26, C28, ..., C60, C70, C2(10+h) ... But these polyhedra were studied much earlier. The distinguished Scottish biologist and classics scholar D’Arcy Thompson (1860–1948) mentioned the Euler formula in connectionwith radiolaria in thefirst, 1917, editionofhis book On Growth and Form [4]. Radiolaria are planktonic microorganisms whose sizes range from 0.04 mm to 1 mm. These fascinating geometrical creatures (Fig. 2) produce their skeletons from mineral compounds absorbed from seawater. Radiolarian skeletons are light, strong, and stable, the very requirements that led Fuller to his concept of geodesic domes. In later editions, Thompson analyzed the now-called fullerenes in detail, and Kroto, et al., cited his work. But was Thompson the first to carry out this analysis? In 2006, while working on my book Fullerenes, Carbon Nanotubes and Nanoclusters: Genealogy of Forms and Ideas [5], I found a reference to a book called Geometry of Radiolaria by Dmitry Morduhai-Boltovskoi, published in Russian in 1936 by

publication date

  • January 1, 2014