Objects with icosahedral symmetry occur in nature only at microscopic scales, including quasicrystals, many viruses, and some beautiful protozoa in the radiolarian family
Image: Simons Foundation Mathematical Impressions
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.
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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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