Wrong icosahedra (29th of April 2011)
I watched the day before yesterday the semi-final of the Champions League and each time when the repeated clip in slow motion
starts, those stars that move really fast toward the viewer appear and below them, a new clip appears. The stars look like a
piece of a soccer ball, yet, as I watch them, something is not right there, something bothers me. As if it is not drawn
correctly. And then I think to myself, c'mon, it has to be correctly drawn, this happening is watched by billon people.
And so, after little bit of research, I concluded that I was right after all. Namely, the logo of the UEFA's Champions League is
really unusual. I mean, it is NOT the representation of a soccer ball as someone might think. On the image above I show on the
left hand side my approximate geometrical construction of the Champions League logo (it is fairly similar to the real logo), and
on the right hand side there is an icosahedral soccer ball than has stars around icosahedral vertices. The difference is obvious,
but the most important thing to note is that the connectivity and topology of the League logo is completely different from
the one required by icosahedral symmetry.
I thought a little bit about the reasons for the observed difference. I don't believe that the designer didn't know how a soccer
ball looks like, besides, she/he could have easily taken it as a template - it seems as there is something else to it. And that
something else may be the dynamics. Namely, in the structure of the League logo one can see a triangle that I painted gray in the
image above. The triangle is skewed, unstable and it gives an impression of motion. In contrast, in the image of real icosahedron,
one can see a fairly stable pentagon which does not have a tendency to move. The logo of the League is much more vibrant than the
geometrically correct representation with the icosahedral symmetry, and that is almost certainly the reason for its "icosahedral
wrongness".
But, since we are here... Below I show you several correct icosahedra, possible designs for soccer balls. It is a good continuation
of a post A la jabulani from the last year, related to the soccer ball of the World Championship.
First, the ball that is used in the League matches:
And then, four possible designs:
DISCLAIMER: This text was made with the sole aim to represent the topology of an icosahedron, and as such, its purpose is primarily educational and noncommercial. The true logo of the Champions League is UEFA's registered trademark. The images I presented are mathematical / geometrical constructions made by modification of a three-dimensional representation of an icosahedral structure.
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Last updated on 29th of April 2011.