Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. IQCs have the highest symmetry of all crystals and therefore exhibit orientationally highly uniform properties. This makes them candidates for materials with a complete photonic bandgap or as specialized alloys. All reported IQCs are intermetallic compounds and either of face-centered-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike other quasicrystals, which have been observed experimentally in micellar or nanoparticle systems and suggested in bi-layer water, silicon, and mesoporous silica, IQCs have not been discussed in the context of non-intermetallic systems. In this contribution, we demonstrate the first self-assembly of an IQC by means of molecular dynamics simulations. The IQC self-assembles rapidly and reproducibly from a fluid phase in a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the-third neighbor shell . It is body-centered icosahedral, and in parameter space neighbors clathrates and other tetrahedrally bonded crystals. We provide a crystallographic structure model and show the presence of a diffusion mechanism not available in periodically ordered solids. Our finding is an important step towards addressing a central remaining question in the theory of crystal growth: How do atoms (or other elementary building blocks) arrange themselves rapidly, and with near structural perfection, into a long-range ordered configuration without the guidance of a unit cell? Finally, we suggest routes to search for the IQC and design it in soft matter and nanoscale systems.  M. Engel, P.F. Damasceno, P.L. Phillips, S.C. Glotzer, Nature Materials, in press (2014).