Icosahedrite

The first quasicrystal (http://en.wikipedia.org/wiki/Quasicrystal) described as a mineral species.

Compare decagoniteAl₇₁Ni₂₄Fe₅, the second natural quasicrystal approved.

Chemically similar to 'Unnamed (Al-Cu-Fe Alloy)'AlCuFe and 'Unnamed (Al-Cu-Fe Alloy II)'Al₇₈Cu₁₅Fe₅.

The vast majority of minerals are crystalline materials, with structures in which a particular arrangement of atoms repeats regularly by translation, like a 3-D wallpaper pattern. Only certain types of rotation axes in the crystal symmetry are compatible with this: 2-fold, 3-fold, 4-fold and 6-fold rotations, and the combination of four 3-fold axes with additional 2- and/or 4-fold axes that gives rise to "cubic" symmetry.

Quasicrystals are a recently discovered type of solid material that use quite different organising principles for arranging their atoms. They do not have an atomic arrangement which repeats regularly by translation, but they do have rotational symmetry about axes which can be of "crystallographically forbidden" orders such as 5-fold, 8-fold, 10-fold and 12-fold, as well as the combination of six intersecting 5-fold axes that is characteristic of the Platonic dodecahedron and icosahedron. Despite the absence of a straightforward, regular repeat unit, they retain a high degree of organisation. Quasicrystalline structures can be made by using more than one type of building block, which fit together via stringent rules so that there are no gaps, no overlaps, but also no repetition. There is still enough regularity in the structure that sharp periodicities occur in the diffraction pattern, albeit with a fractal distribution rather than uniform spacing of frequencies.

Quasicrystal diffraction patterns were first obtained from synthetic aluminium-manganese alloys by Dan Shechtman in 1982, but early observations were regarded with considerable scepticism, even by such eminent crystallographers as Linus Pauling. However, more and more examples were discovered independently by
several research teams, and thermodynamic stability in a quasicrystal alloy was first shown in 1987. Hundreds of synthetic quasicrystal materials are now known, along with chemically similar "approximant" compounds in which regular repeating mistakes convert the quasicrystal atomic arrangement into a normal crystal.

Although quasicrystals can have a well-defined point group ("crystal class") symmetry, they are aperiodic, so other conventional crystallographic concepts such as "lattice type", "space group","unit cell parameters" and "unit cell content" do not apply to the structure as normally considered in three dimensions. However,
it is mathematically possible to generate quasicrystalline structures by taking 3-D slices that are precisely but irrationally oriented through higher-dimensional structures that are periodic: the icosahedral-symmetry quasicrystalline structure of icoashedrite can then be described as a carefully chosen slice through a 6-dimensional hypercubic (hyper)crystal!

In 2011, Dan Shechtman received the Nobel Prize in Chemistry for his discovery of the first quasicrystal. The year previously, Luca Bindi's icosahedrite, the first naturally-occuring quasicrystal, was approved as a new mineral by the Commission on New Minerals and Mineral Classification (IMA 2010-042).

In 2012, Bindi's group published evidence that natural icosahedrite is extraterrestrial in origin. It occurs with other Cu-Al-Fe alloys and a suite of silicates and oxides such as diopsideCaMgSi₂O₆, forsteriteMg₂(SiO₄), spinelMgAl₂O₄ and the extremely high-pressure SiO₂ polymorph stishoviteSiO₂ (which contains icosahedrite as inclusions!). The assemblage and oxygen isotopic composition are consistent with formation not on Earth, but in a refractory calcium-aluminium-rich inclusion in a CV3 chondritic meteorite.

See also Bindi et al. (2022) paper on another - dodecagonal - quasicrystal, Unnamed (Mn-Si-Cr-Al-Ni Quasicrystal)Mn_72.3Si_15.6Cr_9.7Al_1.8Ni_0.6, formed via interaction of a lightning and an eolian dune.