For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit quantum efficiency. However, recent experimental evidence of quantum coherence during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous efforts, the causal connection between coherence and efficiency is still a matter of debate. We show, through extensive simulations of quantum coherent transport on networks, that three dimensional structures characterized by centro-symmetric Hamiltonians are statistically more efficient than random arrangements. Moreover, we theoretical derive a general mechanism for highly efficient quantum transport through nite, disordered 3D networks. It relies on the interplay of disorder with centro-symmetry and a dominant doublet spectral structure, and can be controlled by proper tuning of only coarse-grained quantities. Photosynthetic light harvesting complexes are discussed as potential biological incarnations of this design principle.