A detailed account of the nonmagnetic thermodynamic properties of the two-dimensional, anisotropic, antiferromagnetic, triangular Ising lattice, in the absence of a magnetic field, is presented. The notion of a disorder temperature, TD, is introduced via the exact integral formula for the logarithm of the partition function per spin, and the energy and entropy per spin are evaluated explicitly at TD. Study of the theoretical specific heat curves, and of graphs of the percentage of energy and entropy below the Néel point, shows that the close-packed antiferromagnetic triangular lattice has a qualitatively different behavior from two-dimensional loose-packed lattices. It is suggested that a similar situation will occur in three-dimensional close-packed lattices, and therefore that it is important to use a close-packed Ising model for comparison with experimental data on antiferromagnets which have close-packed lattice structure, or loose-packed lattice structure with higher neighbor interactions.