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In this work, we will show that the concept of nematic order parameter and a generalization of the concept of optical indicatrix, largely used in optics of anisotropic crystals, can be joined to give a new geometrical representation to the anisotropies found in lyotropic liquid crystals. Our theoretical approach will be illustrated using refractive index data of reentrant isotropic-calamitic (discotic) nematic phase transitions of potassium laurate, decanol, and heavy water mixtures. [ABSTRACT FROM AUTHOR]