When adsorbed on solids, water molecules are usually arranged into a honeycomb hydrogen-bond network. Here we report the discovery of a novel monolayer ice built exclusively from water hexamers but without shared edges, distinct from all conventional ice phases. Water grown on graphite crystalizes into a robust monolayer ice after annealing, attaining an exceedingly high density of 0.134 Å^{-2}. Unlike chemisorbed ice on metal surfaces, the ice monolayer can translate and rotate on graphite terraces and grow across steps, confirming its two-dimensional nature. First-principles calculations identify the monolayer ice structure as a robust self-assembly of closely packed water hexamers without edge sharing, whose stability is maintained by maximizing the number of intralayer hydrogen bonds on inert surfaces.