  We present a systematic investigation of the possible locations for the
special point (SP), a unique feature of hybrid neutron stars in the
mass-radius. The study is performed within the two-phase approach where the
high-density (quark matter) phase is described by the constant-sound-speed
(CSS) equation of state (EoS) and the nuclear matter phase around saturation
density is varied from very soft (APR) to stiff (DD2 with excluded nucleon
volume. Different construction schemes for the deconfinement transition are
applied: Maxwell construction, mixed phase construction and parabolic
interpolation. We demonstrate for the first time that the SP is invariant not
only against changing the nuclear matter EoS, but also against variation of the
construction schemes for the phase transition. Since the SP serves as a proxy
for the maximum mass and accessible radii of massive hybrid stars, we draw
conclusions for the limiting masses and radii of hybrid neutron stars.
