This construction is used frequently. It allows, for example, the calculation of inter-limb angles of folds and the angle of unconformity between two sequences of beds.

The solution using the stereographic projection is easy to understand as soon as it is appreciated what is actually meant by the angle between two planes. Figure 17a-17d helps explain this. Planes A and B cut each other to produce a line of intersection, L. The apparent angle between the pair of planes A and B depends on the cross-section chosen to view this angle. For example, the angle α (in Fig. 17a) observed on section plane C (which is perpendicular to the line of intersection) is different to the angle β seen on the oblique section plane (Fig. 17c). In fact, α is the true or dihedral angle between the planes A and B since the dihedral angle between a pair of planes is always measured in the plane which is perpendicular to the line of their intersection.

Determining the dihedral angle between a pair of planes (A, B) stereographically

Method using great circles

1. 1 Plot both planes as great circles (labelled A and B in Fig. 17b).

2. 2 The line of intersection L of these planes is given directly by the point of intersection of the great circles (see p. 26).

3. […]