Geodesic forms

Tarnai, T. (ed.) 1990 Special issue on geodesic forms. Int. J. Space Structures 5, 155-374. Tarnai, T. 1991 The observed form of coated vesicles and a mathematical covering problem. J. molec. Biol. 218, 485-488. 

The calculated electronic structure of Siao indicates [20] that the highest occupied molecular orbital and the lowest xmoccupied molecular orbital display the same symmetry as those of Ceo. In addition the HOMO-LUMO gap is approximately half as large as that for Cm- As predicted for smaller size clusters, the geodesic form is not the most stable structure of Sieo [36]. 

In 1990, a third form of soHd carbon was confirmed and designated TuckniinsterfilUetenes. These 60-carbon (and 78-C) clusters are described as having the shape of a geodesic dome or soccer ball and hence are also known as "bucky balls" (5). 

If you re a sports fan, you ve almost certainly seen this structure before. It is that of a soccer ball with a carbon atom at each vertex. Smalley and his colleagues could have named this allotropic form of carbon "carbosoccer" or "soc-cerene," but they didn t. Instead they called it "buckminster fullerene" after the architect R. Buckminster Fuller, whose geodesic domes vaguely resembled truncated soccer balls. 

In C60 fullerene-type carbon allotrope, there is only one structure in which all the pentagons are nonadjacent and this is icosohedral symmetry-I (Fig. 4.11). This structure is often referred to as backyball to reflect on its full name buckminster-fullerene (after Buckminster Fuller who popularized the geodesic dome as an architectural form). 

This has the form of a geodesic equation [111], and is obeyed by a plane wave. Similarly, we obtain ... 

Until 1985, the only known elemental forms of carbon were diamond, graphite, and amorphous carbon. Then Kroto et al. announced the discovery of C6o, a spherical arrangement of carbon atoms in hexagons and pentagons, as shown in Figure 17.7. They called this form Buckminsterfullerene after the architect Buckminster Fuller, who developed the geodesic dome. The name for this type of carbon molecule has since been shortened to fullerene, but it is commonly called a buckyball. Since this first discovery, it has been found that fullerenes can be made in quantity from electrical arcs between graphite electrodes. About 75% of... 

In this example, Euler s equation takes the form of the geodesic equation... 

The Royal Swedish Academy of Science s press release for the Nobel Prize in Chemistry in 1996 announced The discovery of carbon atoms bound in the form of a ball is rewarded. Buckminsterfullerene (C60), the buckyball, has the same structure as the geodesic dome designed by Buckminster Fuller for the 1996 Montreal World Exhibition. It also has exactly the same structure as a European soccer ball. 

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