Geodesics

The discovery of perfect geodesic dome closed structures of carbon, such as C o has led to numerous studies of so-called Buckminster fullerene. Dislocations are important features of the structures of nested fullerenes also called onion skin, multilayered or Russian doll fullerenes. A recent theoretical study [118] shows that these defects serve to relieve large inherent strains in thick-walled nested fullerenes such that they can show faceted shapes. 

Buckminsterfullerene (Chapter 11 essay Carbon Clusters Fullerenes and Nanotubes ) Name given to the Cgo cluster with structure resembling the geodesic domes of R Buck minster Fuller see front cover... 

Aluminum geodesic dome roof tanks are becoming popular. These are often the economic choice. They offer superior corrosion resistance for a wide range of conditions, and are clear span stmctures not requiring internal supports. They can also be built to any required diameter. However, domes caimot handle more than a few inches of water column internal or external pressure. 

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). 

The C50 molecule contains 12 pentagons and 20 hexagons. This type of hexagonal-pentagonal structure closely resembles the geodesic domes developed by the architect and engineer R. Buckminster Fuller, after whom the molecule is named. In the Csn molecule each carbon atom is bonded to three... 

Al the Ooishi shrine of Ako in Japan, a geodesic dome made of bamboo with three golden balls, which was the symbol called Uraajirushi used by a general named Mori Mis-aemon nojyo Yoshinari at the battle of Okehazama in 1560, has been kept in custody. (See ref. [4]). 

Buckminster Fuller stands in front of a solar-powered geodesic dome house. lAPAA/ide World Photos)... 

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. 

Low angle wrap. Fibers may be placed at different distances from centers at each end when geodesic (nomslipping) path does not have to be followed. 

Polar wrap machine can be used where geodesic (non-slipping) path is in a plane. 

Chemists were greatly surprised when soccer-ball-shaped carbon molecules were first identified in 1985, particularly because they might be even more abundant than graphite and diamond The C60 molecule (10) is named buckminsterfullerene after the American architect R. Buckminster Fuller, whose geodesic domes it resembles. Within 2 years, scientists had succeeded in making crystals of buckminsterfullerene the solid samples are called fullerite (Fig. 14.32). The discovery of this molecule and others with similar structures, such as C70, opened up the prospect of a whole new field of chemistry. For instance, the interior of a C60 molecule is big enough to hold an atom of another element, and chemists are now busily preparing a whole new periodic table of these shrink-wrapped atoms. 

It is useful to test our understanding of determinate structures by considering the simple, yet powerful class of 3-d objects called geodesic structures. These are structures that can be mapped onto the surface of a sphere. There is a beautiful structural theorem about geodesic structures that we will now prove. 

Theorem A geodesic structure is determinate if and only if all of its faces are triangles. 

A geodesic structure with all triangular faces is determinate. 

A geodesic structure with any non-triangular faces is underdetermined, since adding the struts needed to make all faces triangles will add constraints. 

H. Busemann and B. B. Phadke, Spaces with Distinguished Geodesics (1987)... 

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