The concept of three-dimensional (3D) photovoltaics is explored computationally using a genetic algorithm to optimize the energy production in a day for arbitrarily shaped 3D solar cells confined to a given area footprint and total volume. Our simulations demonstrate that the performance of 3D photovoltaic structures scales linearly with height, leading to volumetric energy conversion, and provides power fairly evenly throughout the day. Furthermore, we show that optimal 3D structures are not simple box-like shapes, and that design attributes such as reflectivity could be optimized using three-dimensionality.