Projecting surface of sphere onto plane
The Mercator Projection maps the north and south poles to lines this means that, at these points, the projection is many to one (more about this subject on this page):
Singularities of Euler angles
Simarly we can map Euler angles to quaternions (4 dimensional hypersphere). This maps a one dimensional space (rotations around 0,1,0 axis) to a two dimensional plane in Euler terms. This is where attitude = 90° and heading, bank vary:
On this plane lines of common orientation are diagonal lines, that is rotation around 0,1,0 axis are given by angle = heading+bank.
Similarly for the south pole.
