Gas hydrates are ice-like solids, in which guest molecules or atoms are trapped inside cages formed within a crystalline host framework (clathrate) of hydrogen-bonded water molecules. They are naturally present in large quantities on the deep ocean floor and as permafrost, can form in and block gas pipelines, and are thought to occur widely on Earth and beyond. A natural point of reference for this large and ubiquitous family of inclusion compounds is the empty hydrate lattice, which is usually regarded as experimentally inaccessible because the guest species stabilize the host framework. However, it has been suggested that sufficiently small guests may be removed to leave behind metastable empty clathrates, and guest-free Si- and Ge-clathrates have indeed been obtained. Here we show that this strategy can also be applied to water-based clathrates: five days of continuous vacuum pumping on small particles of neon hydrate (of structure sII) removes all guests, allowing us to determine the crystal structure, thermal expansivity and limit of metastability of the empty hydrate. It is the seventeenth experimentally established crystalline ice phase, ice XVI according to the current ice nomenclature, has a density of 0.81 grams per cubic centimetre (making it the least dense of all known crystalline water phases) and is expected to be the stable low-temperature phase of water at negative pressures (that is, under tension). We find that the empty hydrate structure exhibits negative thermal expansion below about 55 kelvin, and that it is mechanically more stable and has at low temperatures larger lattice constants than the filled hydrate. These observations attest to the importance of kinetic effects and host-guest interactions in clathrate hydrates, with further characterization of the empty hydrate expected to improve our understanding of the structure, properties and behaviour of these unique materials.