Tiling a bathroom floor or a wall mosaic with deep symmetry is pleasing to the eye as the pattern repeats in space. The regular beauty of mineral crystals especially attracts us. Among those crystals there are 32 and only 32 different kinds of symmetries that are possible – only 32 different ways of adding pieces indefinitely to each other in a way that repeats itself, leaves no holes, AND looks the same when you rotate along any of its three directions or axes.
A crystal of table salt had cubic symmetry; it looks the same around each of three axes at right angles to each other. Mathematically it’s been proven that regular crystals can only show symmetry when rotated among 2,3,4, or 6 positions. However, in 1984 Dan Shechtman and 3 colleagues in Israel, France, and the US found a crystal of an aluminum-manganese alloy that had 5-fold symmetry along one axis! It’s what became called a quasicrystal.
Recent Nobel Prize winner and mathematical physicist Roger Penrose predicted them 10 years earlier. Now, Italian geologist Luca Bindi found natural quasicrystals on the Kamchatka Peninsula in Russia in 2012… and they’ve been found at the Trinity Site of the first nuclear weapon. Nature surprises us!
This has been an outreach activity of the Las Cruces Academy, viewable at GreatSchools.org.
Source: Nature, 28 November, pp. 8 17 ff.
