We have developed a new Corner potential suitable for computer simulation studies of pure and mixture systems composed of rodlike, disklike, and spherical molecules. The pair potential is assumed to have the shifted Lennard-Jones 12-6 potential which has the general form of epsilon f(sigma(0)/(r-sigma+sigma(0))) The strength parameter epsilon and the range parameter a are then expanded in terms of a complete orthogonal basis set of functions, called S functions, to obtain expansion coefficients typical of mesogenic molecules. The coefficients,for the range parameter are determined by mapping the expansion onto prolate and oblate spherocylinders which are considered to be more realistic models for rodlike and disklike molecules, respectively. The shape anisotropies considered are (L+D)/D=3 and (D+L)/L=3 for rodlike and disklike molecules, respectively. One of the important advantages of this expansion approach is that each coefficient in the expansion of the strength parameter can be adjusted to reflect the contribution from a specific type of interaction. To make a systematic evaluation of the success of this approach we have obtained, the expansion coefficients for the strength parameter by mapping onto that of two well-studied models: The Gay-Berne (GB) model potential (GBI: mu=1, v=2 and GBII: mu=2, v=1), the potential model for site-site interaction between two molecules each represented by a linear array of four Lennard-Jones centers per molecule (RLJ4). To explore the value of the model potential for studies of liquid crystals, we have carried out a detailed Monte Carlo simulation. We have studied a system of rodlike molecules with shape anisotropy equal to 3 at three packing fractions (Nv(0)/V=0.4, 0.47, and 0.62). Five thermodynamically stable condensed phases have been identified and characterized as crystal, smectic B, smectic A, nematic, and isotropic phases. Such phase polymorphism contrasts with that for a system of hard prolate spherocylinders with the same shape anisotropy which is known to form only isotropic and crystalline phases. The range of stability and the nature of the transition between the phases have been determined. The influence of density on the range and stability of the phases is explored. Increasing the density is found to decrease the range of stability of the nematic phase in favor of the smectic A phase.