We analyze the geometrical states of granular materials by means of a fabric tensor involving the coordination number and fabric anisotropy as the lowest-order descriptors of the contact network. In particular, we show that the fabric states in this representation are constrained by steric exclusions and the condition of mechanical equilibrium required in the quasi-static limit. A simple model, supported by numerical data, allows us to characterize the range of accessible fabric states and the joint evolution of fabric parameters. The critical state in this framework appears as a jammed state in the sense of a saturation of contact gain and loss along the principal strain-rate directions.