Hyperion is Saturn's largest known irregularly shaped satellite and the only moon observed to undergo chaotic rotation. Previous work has identified Hyperion's surface as distinct from other small icy objects but left the causes unsettled. Here we report high-resolution images that reveal a unique sponge-like appearance at scales of a few kilometres. Mapping shows a high surface density of relatively well-preserved craters two to ten kilometres across. We have also determined Hyperion's size and mass, and calculated the mean density as 544+/-50kgm-3, which indicates a porosity of >40 per cent. The high porosity may enhance preservation of craters by minimizing the amount of ejecta produced or retained, and accordingly may be the crucial factor in crafting this unusual surface.