Under high pressure, triply bonded molecular nitrogen dissociates into singly bonded polymeric nitrogen, a potential high-energy-density material. The discovery of stable high-pressure forms of polymeric nitrogen is of great interest. We report the striking stabilization of cagelike diamondoid nitrogen at high pressures predicted by first-principles structural searches. The diamondoid structure of polymeric nitrogen has not been seen in any other elements, and it adopts a highly symmetric body-centered cubic structure with lattice sites occupied by diamondoids, each of which consists of ten nitrogen atoms, forming a N(10) tetracyclic cage. Diamondoid nitrogen possesses a wide energy gap and is energetically most stable among all known polymeric structures above 263 GPa, a pressure that is accessible to a high-pressure experiment. Our findings represent a significant step toward the understanding of the behavior of solid nitrogen at extreme conditions.