Recently there is a suggestion about the star RXJ1856.5−3754, being a possible candidate for quark star. While from the estimates of the radiation radius, given by the authors, it does not seem to fit with any of the known models for such stars, the mass radius diagram admits the possibility of this being a quark star of mass M ⊙ < M < 1.4M ⊙ , provided the radius mentioned is the actual radius...