A two-dimensionally ordered structure of ice crystallized from a glycerol 55% (w/w) aqueous matrix has been studied by adiabatic calorimetry. Its heat capacity was measured between T = 5 K and T = 15 K and found to be consistently larger than that of hexagonal ice (ice Ih) by an average of 1.3%. The composition and the heat capacity of the maximally freeze-concentrated solution, i.e. the non-crystallizing glycerol-rich phase that remains after water's partial crystallization, were also investigated.