Spin ice materials are characterized by a random disorder in the orientation of the moment of the magnetic ions, even when the material is at very low temperatures. Alternating current (AC) magnetic susceptibility measurements find evidence for a dynamic freezing of the magnetic moments as the temperature is lowered somewhat below the temperature at which the specific heat displays a maximum. The broad maximum in the heat capacity does not correspond to a phase transition. Rather, the temperature at which the maximum occurs, about 1 K in Dy 2 Ti 2 O 7, signals a rapid change in the number of tetrahedra where the two-in, two-out rule is violated. Tetrahedra where the rule is violated are sites where the aforementioned monopoles reside. Mathematically, spin ice configurations can be described by closed Eulerian paths.