Since an orientation is determined by its rotation, a set of Euler angles φ₁, Φ and φ₂ uniquely defines an orientation. If we define a space in which the 3 coordinates correspond to the Euler angles, each point in this space represents an orientation.

In general the angles range over 0°≤φ₁≤360°; 0°≤Φ≤180°; 0°≤φ₂≤360°.

However, because of the cubic crystal symmetry of aluminium alloys, and because of the specimen symmetry at rolling, one can reduce the angular range to 0°≤φ₁≤90°; 0°≤Φ≤90°; 0°≤φ₂≤90° in which each orientation occurs at least once.