  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.
