It turns out that we will be able to represent rotations with a unit quaternion. Before looking at why this is so, there are a few important properties to keep in mind:

• The unit quaternions form a three-dimensional sphere in the 4-dimensional space of quaternions.
• Any quaternion can be interpreted as a rotation simply by normalizing it (dividing it by its length).
• Both q and -q represent the same rotation (corresponding to angles of q and 2p - q)