  We present previously unknown solutions to the 3D Gross--Pitaevskii equation
describing atomic Bose-Einstein condensates. This model supports elaborate
patterns, including excited states bearing vorticity. The discovered coherent
structures exhibit striking topological features, involving combinations of
vortex rings and multiple, possibly bent vortex lines. Although unstable, many
of them persist for long times in dynamical simulations. These solutions were
identified by a state-of-the-art numerical technique called deflation, which is
expected to be applicable to many problems from other areas of physics.
