© 2015 Optical Society of America. Due to the increasing interest of polarimetric information in numerous applications, different Stokes polarimeter designs are provided in the literature for the measure of light beam polarization. Recently, the concept of polarimeters based on the conical refraction (CR) phenomenon, occurring in biaxial crystals, was proposed. CR polarimeters are snapshot polarimeters that allow controlling the volume of data redundancy without an increase in the acquisition time. We present the implementation, calibration, and analysis of an incomplete CR-polarimeter optimized for the measure of linear polarizations. A simpler and cheaper experimental configuration is achieved, if compared with other polarimeters proposed in the literature. The suitability of the polarimeter is experimentally demonstrated and some of its benefits, such as its performance in low-intensity conditions, are discussed.