The formation of self-organised structures that resist shear deformation have been discussed in the context of shear jamming and thickening [1][2][3], with frictional forces playing a key role. However, shear induces geometric features necessary for jamming even in frictionless packings [4]. We analyse conditions for jamming in such assemblies by solving force and torque balance conditions for their contact geometry. We demonstrate, and validate with frictional simulations, that the isostatic condition for mean contact number Z = D + 1 (for spatial dimension D = 2, 3) holds at jamming for both finite and infinite friction, above the random loose packing density. We show that the shear jamming threshold satisfies the marginal stability condition recently proposed for jamming in frictionless systems [5]. We perform rigidity percolation analysis [6,7] for D = 2 and find that rigidity percolation precedes shear jamming, which however coincides with the percolation of overconstrained regions, leading to the identification of an intermediate phase analogous to that observed in covalent glasses [8].Jamming is the process by which disordered assemblies of particles become rigid and resist externally imposed stresses, for instance when their density becomes large enough. It has been widely investigated, both as a phenomenon that occurs in granular matter, and as a particular aspect of the emergence of rigidity in disordered matter, e. g. colloidal suspensions, foams, glass formers and gels and to understand the rheological properties of thermal and athermal driven systems [1-3, 5, 9, 10]. The jamming of frictionless sphere assemblies is particularly well studied and occurs at a packing fraction of φ J ≈ 0.64, referred to as random close packing (RCP) or the jamming point. In the presence of friction, jamming is expected to occur down to a significantly lower density, which is ∼ 0.54 (in 3D) [11,12] in the isotropic case, also known as the random loose packing density (RLP), but strong dependences on friction and protocol lead to a wide range of estimates of this density, [0.54 − 0.61]. A rather different scenario was envisaged by Cates et al [13] for jamming in systems subjected to external stress, in which the application of external stress itself leads to a self organisation of particles that could resist stress, and thus lead to jamming. Such a scenario of shear jamming has been studied recently experimentally and theoretically [1,10,14,15] for sheared granular packings in the presence of friction, but also in the case of frictionless spheres [16][17][18][19]. However, our understanding is yet incomplete concerning various central issues, such as: (i) the range of densities over which shear jamming may occur, and the corresponding conditions, (ii) the differences and similarities between shear jamming and the isotropic frictionless as well as frictional jamming, (iii) a geometric description of the self organization of particles that lead to jamming behaviour, and (iv) the origins of the geometric organisation observed...