Inversion and Symmetry Relations for a Three-Dimensional Solvable Model

The solvable sl(n)-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with two- and three-spin interactions. We discuss the spatial symmetry properties of the model and show that its partition function per site obeys the inversion relation. The connection with the free boson model is also discussed.