In this Letter, we present a recipe for the generation of full Poincaré beams that contain all Stokes vortices (SVs), namely ϕ12, ϕ23, and ϕ31 vortices. Superposition of two scalar vortex beams with charges l1 and l2 (where |l1|≠|l2|) in orthogonal states of polarization (SOP) generates all three types of SVs, out of which two types of them are generic and always lie in a ring, with the third type at the center of the ring with index value (l2-l1). Thus, generation of hitherto unknown dark SVs is shown. The number of SVs in a ring is 4|l2-l1|. Index sign inversion for all SVs can be achieved by swapping l1 and l2. By changing the orthogonal pairs of SOPs of the interfering beams, the SV at the center of the ring can be changed from one to another type such that the other two types take part in the formation of the ring of generic SVs. We have also deduced the expressions for the location of all the SVs in the beam. Experimental results are presented.