Sputnik Planitia is a nitrogen-ice-filled basin on Pluto¹. Its polygonal surface patterns² have been previously explained as a result of solid-state convection with either an imposed heat flow³ or a temperature difference within the 10-km-thick ice layer⁴. Neither explanation is satisfactory, because they do not exhibit surface topography with the observed pattern: flat polygons delimited by narrow troughs⁵. Internal heating produces the observed patterns⁶, but the heating source in such a setup remains enigmatic. Here we report the results of modelling the effects of sublimation at the surface. We find that sublimation-driven convection readily produces the observed polygonal structures if we assume a smaller heat flux (~0.3 mW m⁻²) at the base of the ice layer than the commonly accepted value of 2-3 mW m⁻² (ref. ⁷). Sustaining this regime with the latter value is also possible, but would require a stronger viscosity contrast (~3,000) than the nominal value (~100) considered in this study.