  We study the splitting dynamics of giant vortices in dilute Bose-Einstein
condensates by numerically integrating the three-dimensional Gross-Pitaevskii
equation in time. By taking advantage of tetrahedral tiling in the spatial
discretization, we decrease the error and increase the reliability of the
numerical method. An extensive survey of vortex splitting symmetries is
presented for different aspect ratios of the harmonic trapping potential. The
symmetries of the splitting patterns observed in the simulated dynamics are
found to be in good agreement with predictions obtained by solving the dominant
dynamical instabilities from the corresponding Bogoliubov equations.
Furthermore, we observe intertwining of the split vortices in prolate
condensates and a split-and-revival phenomenon in a spherical condensate.
