We present a global ground-state potential energy surface (PES) for the triplet spin state of O4 that is suitable for treating high-energy vibrational-rotational energy transfer and collision-induced dissociation in electronically adiabatic spin-conserving O2-O2 collisions. The surface is based on MS-CASPT2/maug-cc-pVTZ electronic structure calculations with scaled external correlation; the active space has 16 electrons in 12 orbitals. The global ground-state potential energy surface was fitted by a many-body approach with an accurate O-O pairwise interaction and a fit of the many-body interaction potential to 10 180 electronic structure data points. The many-body fit is based on permutationally invariant polynomials in terms of bond-order functions of the six interatomic distances; the bond-order functions are mixed exponential-Gaussian functions. The geometries calculated and used for the fit include geometry scans corresponding to dissociative and vibrationally excited diatom-diatom collisions of O2, scans corresponding to O3 interacting with O, additional geometries identified by running trajectories, and geometries along linear synchronous transit paths connecting randomly selected points. The global O4 PES includes subsurfaces describing the interaction of diatomic molecules with other diatomic molecules or interactions of triatomic molecules and an atom. The interaction of ozone with a ground-state oxygen atom occurs on the triplet O4 surface, and our surface includes high-energy points with O3-O geometries as well as O2-O2 geometries and O2-O-O geometries.