### What it is

Gonbad-e Qābus (Blue Tower Mausoleum) was built by Seljuk Turks in 1196-1197 at the southwest of Iran. Bizarre geometric pattern brought scientists’ attention to this tower.

### What scientists think about it

This is the earliest example of non-periodic pattern with fivefold symmetry and the long-range order. Until recent times, it was thought that these patterns were invented by famous British mathematician Roger Penrose in 1974. Penrose’s insight was considered genius, as later in 1982, Israeli scientist Dan Shechtman discovered quasicrystals, the structure of which is described by Penrose mosaics. All of the known quasicrystals (several hundred) are alloys by their nature, originally synthetic. In 2009, a first natural quasicrystal, named ‘icosahedron’ was found in Chukotka.

Penrose had patented his mosaics and in 1997 he won a lawsuit against *Kleenex* company, which produced a toilet paper with Penrose mosaic stamping. At that time, patterns of Blue Tower were not widely known, otherwise Penrose would not be able to patent his mosaic and win the court case. Nowadays, quite many examples of such quasicrystal patterns are known, and they were made by Islamist artist in Medieval.

From a scientific point of view, quasicrystals are extremely interesting. Despite winning the Nobel prize in chemistry in 2011 for the discovery of quasicrystals, back in 1982, Shechtman had to stand hard for his work and fight for it, as nobody really believed in it. In fact, the symmetry characteristic for quasicrystals (comprising axis of fifth, tenth or eighth or twelfth order), that have been discovered by him, does not mathematically match to periodicity, which is typically seen in crystals. It turned out that quasicrystals display a highly-ordered non-periodic structure and contain elements of symmetry, that are impossible in periodic crystals. Penrose mosaic is the simplest model of quasicrystal structure. Interestingly, the growth process of quasicrystals is still unclear. More precise models present quasicrystals as three-dimensional sections of multidimensional(4-6-dimensional) periodic crystals, however there is still no reliable definition of quasicrystals structure.

### Why one should know about it

The history of Blue tower, Penrose mosaics and quasicrystals shows the unexpected connection between art, mathematics and chemistry.This story also demonstrates that modern science deals with many unsolved fundamental questions.

Professor of Crystallography, Computational Materials Discovery Laboratory, Stony Brook University

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