The canonical ensemble Monte Carlo method is used to study the adsorption of Xe atoms inside of a zeolite alpha cage. The cage is modeled in 2 ways: 1) as atoms placed on the vertices and line segments of a polyhedron and, and 2) as atoms placed in their crystallographically determined positions. Discrete adsorption sites are found and they change position in response to changes in loading, cage cation content, and cage model. Thermodynamic data determined from the crystallographic model cage is in good agreement with experiment, while data obtained from the polyhedral model is only qualitatively correct. In this way we show that, in order to model adsorption in zeolites accurately, it is important to account for the precise architecture of the pore.