Geometrically frustrated self-assembly of hyperbolic crystals from icosahedral nanoparticles.

Geometric frustration is a fundamental concept in various areas of physics, and its role in self-assembly processes has recently been recognized as a source of intricate self-limited structures. Here we present an analytic theory of the geometrically frustrated self-assembly of regular icosahedral nanoparticle based on the non-Euclidean crystal {3,5,3} formed by icosahedra in hyperbolic space. By considering the minimization of elastic and repulsion energies, we characterize prestressed morphologies in this self-assembly system. Notably, the morphology exhibits a transition that is controlled by the size of the assembled cluster, leading to the spontaneous breaking of rotational symmetry.