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We explore the possible mass radius relation of compact stars for theequation of states with a first order phase transition. The low density matteris described by a nuclear matter equation of state resulting from fits tonuclear properties. A constant speed of sound parametrization is used todescribe the high density matter phase with the speed of sound $c_s^2=1$.  A classification scheme of four distinct categories including twin starsolutions, i. e. solutions with the same mass but differing radii, is foundwhich are compatible with the $M \ge 2M_\odot$ pulsar mass constraint.  We show the dependence of the mass and radius differences on the transitionparameters and delineate that higher twin star masses are more likely to beaccompanied by large radius differences. These massive twin stars are generatedby high values of the discontinuity in the energy density and the lowestpossible values of the transition pressure that still result in masses of $M\geq 2M_\odot$ at the maximum of the hadronic branch.

Classifications of Twin Star Solutions for a Constant Speed of Sound Parameterized Equation of State