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Neutrons are encountered in many different fields, including condensed matter physics, space exploration, nuclear power, and healthcare. Neutrons interacting with a biological target produce secondary charged particles that are damaging to human health. The most effective way to shield neutrons is to slow them to thermal energies and then capture the thermalized neutrons. These factors lead us to consider potential materials solutions for neutron shields that maximize the protection of humans while minimizing the shield mass, and which adapt well to modern additive manufacturing techniques. Using hexagonal boron nitride (hBN) as a capture medium and high-density polyethylene (HDPE) as a thermalization medium, we aim to design the optimal internal structure of h$^{10}$BN/HDPE composites by minimizing the effective dose, which is a measure of the estimated radiation damage exposure for a human. Through Monte Carlo simulations in Geant4, we find that the optimal structure reduces the effective dose up to a factor of 72x over aluminum (Al) and 4x over HDPE; this is a significant improvement in shielding effectiveness that could dramatically reduce the radiation exposure of occupational workers.