Subsidence of implants into bone is a major source of morbidity. The underlying mechanics of the phenomenon are not clear, but are likely related to interactions between contact stresses and the underlying porous trabecular bone structure. To gain insight into these interactions, we studied the penetration of three-dimensional (3D)-printed indenters with systematically varying geometries into Sawbones® foam substrates and isolated the effects of contact geometry from those of overall contact size and area. When size, contact area, and indented material stiffness and strength are controlled for, we show that resistance to penetration is in fact a function of topology only. Indenters with greater line contact lengths support higher subsidence loads in compression. These results have direct implications for the design of implants to resist subsidence into bone.