Icosahedral twinning has been seen in face-centered-cubic metal nanoparticles that have nucleated: (i) by evaporation onto surfaces, (ii) out of solution, and (iii) by reduction in a polymer matrix.
Quasicrystals are un-twinned structures with long range rotational but not translational periodicity, that some initially tried to explain away as icosahedral twinning. Quasicrystals generally form only when the compositional makeup (e.g. of two dissimilar metals such as titanium and manganese) serves as an antagonist to formation of one of the more common close-packed space-filling forms.