Silver iodide is one of the most effective ice nuclei known. We use molecular dynamics simulations to investigate ice nucleation by AgI disks and plates with radii ranging from 1.15 to 2.99 nm. It is shown that disks and plates in this size range are effective ice nuclei, nucleating bulk ice at temperatures as warm as 14 K below the equilibrium freezing temperature, on simulation time scales (up to a few hundred nanoseconds). Ice nucleated on the Ag exposed surface of AgI disks and plates. Shortly after supercooling an ice cluster forms on the AgI surface. The AgI-stabilized ice cluster fluctuates in size as time progresses, but, once formed, it is constantly present. Eventually, depending on the disk or plate size and the degree of supercooling, a cluster fluctuation achieves critical size, and ice nucleates and rapidly grows to fill the simulation cell. Larger AgI disks and plates support larger ice clusters and hence can nucleate ice at warmer temperatures. This work may be useful for understanding the mechanism of ice nucleation on nanoparticles and active sites of larger atmospheric particles.