  Characterizing and localizing electronic energy degeneracies is important for
describ-ing and controlling electronic energy flow in molecules. We show, using
topological phase considerations that the Renner effect in polyatomic molecules
with more than 3 nuclei is necessarily accompanied by 'satellite' conical
intersections. In these intersections the non-adiabatic coupling term is on the
average half an integer. We present ab-inito results on the tetra-atomic
radical cation C2H2+ to demonstrate the theory
