Eutectic behavior and the induced crystalline phase in mixtures of hexagonal columnar liquid crystal, 2, 3, 6, 7, 10, 11-hexakis-(pentyloxy) triphenylene (HPTP)/reactive mesogenic diacrylate monomer, 4-(3-acryloyloxypropyloxy)-benzoic acid 2-methyl-1,4-phenylene ester (RM257) have been investigated both experimentally and theoretically. To determine the theoretical phase boundaries, we combined the free energy of Flory-Huggins free energy for liquid-liquid demixing, Maier-Saupe free energy of nematic ordering, and Chandrasekhar-Clark free energy of hexagonal ordering. The calculated phase diagram of the HPTP/RM257 blend is essentially of a eutectic type that consists of isotropic (I), nematic (N), and hexagonal columnar (Col(h)) regions, and nematic isotropic (N+I), hexagonal columnar + isotropic (Col(h)+I), and hexagonal columnar + nematic (Col(h)+N) coexistence regions, bound by the liquidus and solidus lines. Of particular interest is the formation or an induced crystalline phase (Cr-in) in the intermediate compositions of the HPTP/RM257 mixtures, exhibiting Cr-2 (RM257) + Cr-in in the RM257-rich and Cr-in + Cr-1 (HPTP) in the HPTP-rich regions.