We experimentally investigate the effect of geometrical anisotropy for buoyant ellipsoidal particles rising in a still fluid. All other parameters, such as the Galileo number $Ga approx 6000$ and the particle density ratio $Gamma approx 0.53$ are kept constant. The geometrical aspect ratio, $chi$, of the particle is varied systematically from $chi$ = 0.2 (oblate) to 5 (prolate). Based on tracking all degrees of particle motion, we identify six regimes characterised by distinct rise dynamics. Firstly, for $0.83 le chi le 1.20$, increased rotational dynamics are observed and the particle flips over semi-regularly in a tumbling-like motion. Secondly, for oblate particles with $0.29 le chi le 0.75$, planar regular zig-zag motion is observed, where the drag coefficient is independent of $chi$. Thirdly, for the most extreme oblate geometries ($chi le 0.25$) a flutter-like behaviour is found, characterised by precession of the oscillation plane and an increase in the drag coefficient. For prolate geometries, we observed two coexisting oscillation modes that contribute to complex trajectories: the first is related to oscillations of the pointing vector and the second corresponds to a motion perpendicular to the particles symmetry axis. We identify a longitudinal regime ($1.33 le chi le 2.5$), where both modes are active and a different one, the broadside-regime ($3 le chile 4$), where only the second mode is present. Remarkably, for the most prolate particles ($chi = 5$), we observe an entirely different helical rise with completely unique features.
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