  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.
