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The authors investigate the phase diagram of a three-dimensional associating lattice gas (ALG) model. This model combines orientational icelike interactions and “van der Waals” that might be repulsive, representing, in this case, a penalty for distortion of hydrogen bonds. These interactions can be interpreted as two competing distances, making the connection between this model and continuous isotropic soft-core potentials. The authors present Monte Carlo studies of the ALG model showing the presence of two liquid phases, two critical points, and density anomaly.