Heterogeneous ice nucleation has a key role in fields as diverse as atmospheric chemistry and biology. Ice nucleation on metal surfaces affords an opportunity to watch this process unfold at the molecular scale on a well-defined, planar interface. A common feature of structural models for such films is that they are built from hexagonal arrangements of molecules. Here we show, through a combination of scanning tunnelling microscopy, infrared spectroscopy and density-functional theory, that about 1-nm-wide ice chains that nucleate on Cu(110) are not built from hexagons, but instead are built from a face-sharing arrangement of water pentagons. The pentagon structure is favoured over others because it maximizes the water-metal bonding while maintaining a strong hydrogen-bonding network. It reveals an unanticipated structural adaptability of water-ice films, demonstrating that the presence of the substrate can be sufficient to favour non-hexagonal structural units.