Example of the relation between the various EOS parameters and properties of the twin branch. The state of matter at the phase transition point (here quantified by the dM/dR slope on the M(R) plane) is related to the parameters of the interior EOS. For the DB and DR EOS M_max >  M_ph; for the R and B EOS M_max = M_ph; for the O and C EOS M_max <  M_ph; for the Y EOS there are no stable twin solutions.