Scanning tunneling microscopy (STM) images of water submonolayers on Pd(111) reveal quasiperiodic and isolated adclusters with internal structure that would ordinarily be ascribed to icelike puckered hexagonal units. However, density functional theory and STM simulations contradict this conventional picture, showing instead that the water adlayers are composed mainly of flat-lying molecules arranged in planar water hexagons. A new rule for two dimensional (2D) water growth is offered that generates the structures observed experimentally from planar hexamer units.