Sunday, July 6, 2014

The Brazuca and octahedral fullerenes

Yuan-Jia and I submitted a manuscipt entitled, From the "Brazuca" ball to Octahedral Fullerenes: Their Construction and Classification, to the physics preprint archive, arXiv, recently. Basically, we observed that the symmetry of the Brazuca ball used in the FIFA World Cup held now in Brazil is exactly that of an octahedral fullerene, which Yuan-Jia has been thinking about for more than a year. Therefore, we modified the original manuscript a little bit to point out this peculiar connection. Hopefully, researchers can know that not only the original the Adidas Telstar, a truncated icosahedron, has a microscopic analog, namely the famous C60, the current Brazuca ball could also have microscopic correspondence, in principle.

The Adidas Telstar vs a C60 molecule

The Adidas Brazuca vs an octahedral fullerene

Here I give a list of symmetry groups for all official match footballs (soccer balls) adopted by the FIFA since 1970:

Year Country Name of the official match ball Point group
1970 Mexico The Adidas Telstar Ih
1974 West Germany The Adidas Telstar Durlast Ih
1978 Argentina The Adidas Tango Durlast Ih
1982 Spain The Adidas Tango Espana Ih
1986 Mexico The Adidas Azteca Ih
1990 Italy The Adidas Etrvsco Ih
1994 USA The Adidas Questra Ih
1998 France The Adidas Tricolore Ih
2002 Korea Japan The Adidas Fevernova Ih with T pattern
2006 Germany The Adidas Teamgeist Th
2010 South Africa The Adidas Jabulani Td
2014 Brazil The Adidas Brazuca O

It is interesting to note that it took FIFA 28 years to move away from the icosahedral symmetry to the tetrahedral symmetry, and then another 12 years to come to the last of three Platonic symmetry groups, namely the octahedral group. Another peculiar difference between the Brazuca ball and the previous soccer balls is the lack of inversion and mirror symmetries in the Brazuca ball, meaning that the Brazuca ball is chiral. This should lead to nonvanishing coupling between translational and rotational (spinning) motions, I suspect.

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