Is it safe to say that 3d objects only have 2 and 1/2 rotations

So I've been getting into the math behind animations in video games, specifically Quaternions; and I've noticed that when extracting Euler Angles from a Quaternion, the Yaw is limited from $-90$ to $90$ while Pitch and Roll both get a full $-180$ to $180$. Since a Quaternion can describe every rotation in $3$ dimensions, would it be correct to say that 3d objects only need $2$ and $1/2$ angles to describe them?