Chiral domes and Buckminster Fuller, 21st of December 2009.

Zagreb got white during the weekend, and my eyes only saw white when the computer I used for research and coding during the whole years of 2007 and 2008 started acting weirdly. The tragic story that ended semi-tragically, but I won't speak about that any further. I'll speak about the examination of data backups that I was forced to do due to that unfortunate situation. I found all sorts of things, time does fly as they say and our faces change. I won't speak about that also any further, I guess that the snow outside makes me sentimental. Anyhow. I found some really nice images since the times of Nanoatlas. The story I want to tell you is about chiral geodesic domes.

Buckminster Fuller was an inventor, designer, architect and visionary that I was writing about several times. Geodesic domes are an invention of his that cemented his name in history. Namely, Harry Kroto, winner of the Nobel prize for the discovery of fullerenes, whom I had the opportunity to listen to in flesh, said that he was inspired by Fuller's geodesic domes while he was determining the structure of C₆₀ molecules. Therefore, it is not strange that the C₆₀ molecule got the name buckminsterfullerene, and the whole family of cage-like molecules made of carbon the name got the name fullerenes (see the image below which show three of the so-called icosahedral fullerenes). The story goes beyond this - not only that Kroto was inspired by geodesic dome design, it can in fact be shown that fullerenes and geodesic domes are linked in a clear and direct mathematical way. I wrote a paper on that which you can download and read HERE.

In short, the geodesic domes are polyhedra that can be obtained iteratively from some starting polyhedron so that in the larger order of iteration they become more similar to the sphere. In the Fuller sense, this was not enough, and he also wanted that all edges of the polyhedron are as similar in length as possible so that such domes can be simply and modularly constructed. But the conditions that the edges are as similar in length as possible and that the polyhedron is a good approximation of the sphere are not at all easily satisfied simultaneously.

Fuller didn't realize that the class of domes he envisioned contains a special type that is chiral, which means that they are not equal to their mirror image. There are, of course, infinite number of these, and they can be described, as all other geodesic domes, with two non-negative integers. If the two integers are not the same, and none of them is zero, the domes are chiral - one can see thus that in the set of all the geodesic domes, there is a largest number of chiral ones (let's not talk about the ratios of infinities here).

And so, the snow has covered the hill (this rhymes in Croatian), my data melted before its time, but what's important is that something of it stayed in my head, what can you do. As a gift and an appropriate visual information in these holydays, I offer you semi-transparent glass-metal balls for the christmas tree in the form of chiral geodesic domes.

Oh, yes, I forgot. Of course, the mathematics of viruses is the same as the mathematics of geodesic domes. To prove this, in the image below I show (this time non-chiral) geodesic dome around the turnip yellow mosaic virus.

There is a history of everything and even of seemingly most irrelevant things.

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Last updated on: 21st of December 2009.