The present paper reports on molecular dynamics simulations of the formation process of Si quantum dots ͑Si QDs͒. Icosahedral Si QDs are formed spontaneously by freezing 274-, 280-, and 323-atom Si droplets. We find that the initialization of pentagonal channels leads into the overall icosahedral structure. We also study the melting behavior of the 280-atom icosahedral Si QD. We find that the melting point is reduced more than 15% compared with that of bulk Si. A possible approach to synthesize icosahedral Si QDs is discussed. The formation of the icosahedral structure could be expected in other systems characterized by tetrahedral bonding network.