Planetary nebulae—the ejected envelopes of red giant stars—provide us with a history of the last, mass-losing phases of 90% of stars initially more massive than the Sun. Here we analyse images of the planetary nebula NGC 3132 from the James Webb Space Telescope (JWST) Early Release Observations. A structured, extended hydrogen halo surrounding an ionized central bubble is imprinted with spiral structures, probably shaped by a low-mass companion orbiting the central star at about 40-60 au. The images also reveal a mid-infrared excess at the central star, interpreted as a dusty disk, which is indicative of an interaction with another closer companion. Including the previously known A-type visual companion, the progenitor of the NGC 3132 planetary nebula must have been at least a stellar quartet. The JWST images allow us to generate a model of the illumination, ionization and hydrodynamics of the molecular halo, demonstrating the power of JWST to investigate complex stellar outflows. Furthermore, new measurements of the A-type visual companion allow us to derive the value for the mass of the progenitor of a central star with excellent precision: 2.86 ± 0.06 M⊙. These results serve as pathfinders for future JWST observations of planetary nebulae, providing unique insight into fundamental astrophysical processes including colliding winds and binary star interactions, with implications for supernovae and gravitational-wave systems.