To understand its evolution and the effects of its eruptive events, the Sun is permanently monitored by multiple satellite missions. The optically-thin emission of the solar plasma and the limited number of viewpoints make it challenging to reconstruct the geometry and structure of the solar atmosphere; however, this information is the missing link to understand the Sun as it is: a three-dimensional evolving star. We present a method that enables a complete 3D representation of the uppermost solar layer (corona) observed in extreme ultraviolet (EUV) light. We use a deep learning approach for 3D scene representation that accounts for radiative transfer, to map the entire solar atmosphere from three simultaneous observations. We demonstrate that our approach provides unprecedented reconstructions of the solar poles, and directly enables height estimates of coronal structures, solar filaments, coronal hole profiles, and coronal mass ejections. We validate the approach using model-generated synthetic EUV images, finding that our method accurately captures the 3D geometry of the Sun even from a limited number of 32 ecliptic viewpoints ($|\text{latitude}| \leq 7^\circ$). We quantify uncertainties of our model using an ensemble approach that allows us to estimate the model performance in absence of a ground-truth. Our method enables a novel view of our closest star, and is a breakthrough technology for the efficient use of multi-instrument datasets, which paves the way for future cluster missions.
