A sphere is completely rotationally symmetrical in all directions. You can apply any combination of roll, pitch and yaw to it and it would be indistinguishable from the sphere you started with.
A cylinder is rotationally symmetrical along its "long" axis but if you rotate it in the other 2 directions, it becomes distinguishable from the original.
I am wondering if there exists a shape that has 2 axis of continuous rotational symmetry. A shape that could roll and pitch and be identical to the original but breaks symmetry if a yaw is applied.