Definition of the Hot Water World triangles (light blue) in the mass–radius space. The left panel shows mass–radius models generated using the BICEPS forward model (Haldemann et al. 2024), for a fixed equilibrium temperature of 900 K. We generated models for three different core compositions, an iron-less, purely rocky core (in purple), an Earth-like core (33% inner iron core, 67% silicate mantle, in pink), and a Mercury-like core (70% inner iron core, 30% silicate mantle, in green). For each of these core compositions, we then show three different mass–radius relations, one assuming a bare core (solid lines), one with a 1% H/He envelope (dotted lines), and one with a 50% steam atmosphere (dashed lines). The three panels on the right show the temperature dependence of the Hot Water World triangles, with the same mass–radius relations as before now generated for different equilibrium temperatures of 600 K (top), 1200 K (middle), and 1800 K (bottom). See text for further details.