The control of spatial and polarization modes of optical beams enables the production of topological singularities encoded on the polarization of the light. This allows the study of topological disclinations not easily found in the natural setting. In this article we report on the observation of new features in disclinations realized with singular optical beams. They were prepared using three spatial modes bearing optical vortices in non-separable superpositions with circular polarization states. The disclinations involve asymmetric rotational dislocations, whose optical counterparts in the optical far field are known as C-points, and which are classified as monstars. They have been known to have a singularity index that can be positive, or negative as reported by us recently. Here we report on monstars with an index of zero. Monstars are characterized by having sectors bound by radial lines that involve curved lines radiating from the singularity. We found that kinks in otherwise smooth line patterns of asymmetric disclinations are scars of a separate but related pattern of line-slope discontinuities, carried optically by C-lines in the far field. These scars are indicative of the underlying structure or symmetry of the pattern. We present a general formalism to understand and generate monstars, along with measurements: The experimental results are in excellent agreement with theoretical modelings.