In this work, we report on the direct visualization of magnetic structure in sculpted three-dimensional cobalt (Co) nanospirals with a wire diameter of 20 nm and outer spiral diameter of 115 nm and on the magnetic interactions between the nanospirals, using aberration-corrected Lorentz transmission electron microscopy. By analyzing the magnetic domains in three dimensions at the nanoscale, we show that magnetic domain formation in the Co nanospirals is a result of the shape anisotropy dominating over the magnetocrystalline anisotropy of the system. We also show that the strong dipolar magnetic interactions between adjacent closely packed nanospirals leads to their magnetization directions adopting alternating directions to minimize the total magnetostatic energy of the system. Deviations from such magnetization structure can only be explained by analyzing the complex three-dimensional structure of the nanospirals. These nanostructures possess an inherent chirality due to their growth conditions and are of significant importance as nanoscale building blocks in magneto-optical devices.