  We determine the phase diagram for a generalisation of two-and
three-dimensional hard spheres: a classical system with three-body interactions
realised as a hard cut-off on the mean-square distance for each triplet of
particles. Quantum versions of this model are important in the context of the
unitary Bose gas, which is currently under close theoretical and experimental
scrutiny. In two dimensions, the three-body hard-core model possesses a
conventional atomic liquid phase and a peculiar solid phase formed by dimers.
These dimers interact effectively as hard disks. In three dimensions, the solid
phase consists of isolated atoms that arrange in a simple-hexagonal lattice.
