The fundamental structure of the full set of solutions of the BCS P-3(
2) pairing problem in neutron matter is established. The relations bet
ween different spin-angle components in these solutions are shown to b
e practically independent of density, temperature, and the specific fo
rm of the pairing interaction. The spectrum of pairing energies is fou
nd to be highly degenerate. [S0031-9007(98)07563-2].