Polynitrogen compounds have attracted great interest due to their potential applications as high energy density materials. Most recently, a rich variety of alkali polynitrogens (RxNyi; R = Li, Na, and Cs) have been predicted to be stable at high pressures and one of them, CsN5 has been recently synthesized. In this work, various potassium polynitrides are investigated using first-principles crystal structure search methods. Several novel molecular crystals consisting of N-4 chains, N-5 rings, and N-6 rings stable at high pressures are discovered. In addition, an unusual nitrogen-rich metallic crystal with stoichiometry K2N16 consisting of a planar two-dimensional extended network of nitrogen atoms arranged in fused 18 atom rings is found to be stable above 70 GPa. An appreciable electron transfer from K to N atoms is responsible for the appearance of unexpected chemical bonding in these crystals. The thermodynamic stability and high pressure phase diagram is constructed. The electronic and vibrational properties of the layered polynitrogen K2N16 compound are investigated, and the pressure-dependent IR spectrum is obtained to assist in experimental discovery of this new high-nitrogen content material.