A la jabulani (29th of June 2010)

Jabulani in Zulu languange means "brings joy and happines". It is often used as (male?) first name, Jabu in a shortened variant.

The word has been used as a name for the match ball of the 2010 FIFA World Cup produced by Adidas. It is a nice looking ball, and the first thing that got into my eye is that the ball ornament has the tetrahedral symmetry. I played a bit with the ornaments, african colorfulness, and symmetry and I made several images centered around the a la Jabulani theme. In the image that opens this post one can see the ball with tetrahedral symmetry of its ornament, somewhat similar, and yet, deliberately different from the "real" Jabulani. The background is not african, it is a panoramic photograph constructed from several shots taken from a hill in Croatian Zagorje region. The flowers in the grass are called African daisies (or Gousblom in Afrikaans), and the model I made is closest to genus Arctotis. I experimented a lot with the flowers and I made several variants. One of them is shown below.

Soccer balls are known for their interesting symmetry, and everyone knows that the "old fashioned" soccer ball and buckminsterfullerene molecule (made of 60 carbon atoms) have the same symmetry - they are truncated icosahedra with characteristic pentagons and hexagons. One can make all sorts of different things on a sphere surface and use all sorts of polyhedra to form an ornament. Thus, in a real Jabulani one can see a tetrahedron, as one can also in the image below.

One can of course do it differently. For example, instead of tetrahedral, one can construct an octahedral ornament. Such a variant is shown in the image below.

Soccer balls are most often of the icosahedral (or dodecahedral - these two are dual) symmetry. One such "african" ball is shown in the image below.

One can completely abandon the polyhedra and construct the ball out of a sphere and two mutually perpendicular tori, as shown below.

Certainly the most interesting ball in this series is shown in the image below. The ornament is made of two completely equal parts - two "frogs" that bite each other's "tails". It is difficult to see this from the two projections, I should animate the object. In any case, it is a kind of sphere covering using complex shapes. It has some similarity to what M.C. Escher did in a plane and I also played with it in "Problem of the observer" (the image that shows covering of the plane with eagles and tortoises).

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Last updated on 29th of June 2010.