Poincare Sphere Canonical Target Locations

If a dihedral is a double/even bounce and a trihedral is a single/odd bounce target then why are their locations on the Poincare sphere on the equator? In this article, Besic et al., Poincare Sphere Representation Of Independent Scattering Sources: Application On Distributed Targets (https://www.researchgate.net/publication/260821542_Poincare_Sphere_Representation_Of_Independent_Scattering_Sources_Application_On_Distributed_Targets) indicates so.

As per the Poincare sphere distribution of the polarization ellipses shouldn’t these scattered be on the north and south poles respectively to say that the same sense is scattered by the dihedral and opposite sense by the trihedral targets?

I am not familiar with this concept, sorry.