We investigate theoretically a novel experimental polymer route to C3N4 materials. Starting with simple molecules, we follow the initial steps of oligomerization of several carbodiimide based C3N4 precursors. A sequence of hypothetical models with a chemically resonable structure for the resulting low-density C3N4 polymers is constructed. Simulating high pressures, we show that one hypothetical polymer structure might undergo a polymorphic transition into cubic C3N4 Another one is transformed into a novel dense 3/4-connected C3N4 structure with odd-membered rings and C-C and N-N bends.