Multifunctional sandwich panels with corrugated and prismatic diamond cores have been analyzed and their behavior compared with panels designed using truss and honeycomb cores. Failure mechanism maps have been devised that account for interactions between core and face members during buckling. The optimal dimensions and the minimum weight have been evaluated. The load capacities predicted for near-optimal designs have been validated by conducting selected finite element calculations. Designs that use diamond prismatic cores (with corrugation order 4) are slightly more weight efficient than trusses, when optimized for a specific loading direction. Honeycomb cores, while somewhat more weight efficient, especially at lower load capacities, are not amenable to the fluid flows needed for cooling. We conclude that the diamond prismatic topology is the most weight efficient among designs amenable to simultaneous load bearing and active cooling.