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From Simons Science News (find original story here).
Mathematicians classify objects by their symmetries. If you turn a five-armed starfish a fifth of a revolution, it looks unchanged, so it has a five-fold rotational symmetry axis. Objects like a soccer ball, which has five-fold rotation axes (through the black pentagons) and three-fold rotation axes (through the white hexagons), are said to have “icosahedral symmetry.” The arrangement of rotations which leave the objects looking unchanged is the same as that of a regular icosahedron.
It is an unexplained fact that objects with icosahedral symmetry occur in nature only at microscopic scales. Examples include quasicrystals, many viruses, the carbon-60 molecule, and some beautiful protozoa in the radiolarian family. Luckily, we humans can make our own human-scale examples, so everyone can see and appreciate this lovely symmetry group. However, nature’s radiolarian examples are the most stunning instances of icosahedral symmetry and well worth a careful look.
Credits:
Radiolarian images from Ernst Haeckel’s “Art Forms in Nature,” 1899–1904.
Quasicrystal images from Wikipedia and Stanford University.
Virus images from Virusworld.
Related:
More videos from the Mathematical Impressions series.
Reprinted with permission from Simons Science News, an editorially-independent division of SimonsFoundation.org whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the computational, physical and life sciences.
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5 Comments
Add CommentI just wanted to say what a delightful video this was. I had no idea the Platonic solids occurred so frequently in nature, nor that they formed three families of duals.
Reply | Report Abuse | Link to thisI had a candle burning beside me when the video announced that carbon buckyballs were being produced. Made me look twice at the flame, and I peered at it as if being a foot away was the thing preventing me from seeing them.
Lovely work.
It makes me sad though that Earnest Haeckel resorted to fraud in his efforts to promote evolution. Ontology does not recapulate phylogeny.
Reply | Report Abuse | Link to thismis-spelled, meant recapitulate.
Reply | Report Abuse | Link to thisDon't be sad secretagent3180, the fraud allegations were most likely totally unfounded to begin with and the theory of Evolution is as strong as it ever was.
Reply | Report Abuse | Link to thisActually, I clicked on this article accidentally, but it is very interesting and enjoyable. I had no idea that candle soot contained buckminsterfullerene particle-waves!
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