60: Something Special
The Babylonians had a counting system based on the interesting number 60. Not coincidentally, there is that number of seconds in a minute and 60 of the latter in an hour. 60 is the smallest number to have 1, 2, 3, 4, 5 and 6 as its divisors and it is also the smallest number with 12 factors. There are also 60 carbon atoms in a highly innovative synthetic molecule known as buckminsterfullerene. It is shaped like a soccer ball with pentagonal and hexagonal faces. Each of the 60 carbon atoms is a vertex on both a pentagon and a hexagon, but none of the pentagons are adjacent to each other, so there are 60/5 = 12 pentagons.
Each pentagon is attached to 5 hexagons but each hexagon is shared by 3 pentagons, so there are 12(5)/3 = 20 hexagons.
The structure follows Euler's polyhedron formula, |V|-|E|+|F| = 2, (where |V|, |E|, |F| indicate the number of vertices, edges, and faces). If we apply the formula to C60 :
60 – E + (20 + 12) = 2
E = 90, so the molecule has ‘90 edges’.
Only after it was synthesized (in 1985) was it realized that C60 is found in candle soot.
Fullerenes such as C60 are formed when vaporized carbon condenses in a noble gas atmosphere. The gaseous carbon can be obtained by directing an intense pulse of laser light at carbon’s surface. The released carbon atoms are mixed with a stream of helium gas and combine to form clusters of up to hundreds of atoms. It took about five years after the initial discovery to make appreciable quantities of the compound, and it became apparent that this discovery would father a fair amount of new chemistry.
Hugh Aldersey-Williams. The
Most Beautiful Molecule: An Adventure in Chemistry, Aurum Press.