The HI homodimer was found to have structural and vibrational properties unlike any other previously studied (HX)(2) system, with X = F, Cl, and Br. The infrared spectrum of (HI)(2) is also observed to be distinctly different from the other members of the series. In addition, the interaction energy of the (HI)(2) dimer has been calculated using the coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] level of theory. A four-dimensional morphed intermolecular potential has been generated and then morphed using available near infrared and submillimeter spectroscopic data recorded in supersonic jet expansions. The morphed potential is found to have a single global minimum with a symmetric structure having C(2h) symmetry. The equilibrium dissociation energy is found to be 359 cm(-1) with the geometry in Jacobi coordinates of R(e) = 4.35 Å, θ(1) = 43°, θ(2) = 137°, and φ = 180°. The infrared spectrum is characterized by pairs of excited vibrational states resulting from the coupling of the two HI stretching modes. A qualitative model using a quadratic approximation has been fitted to obtain an estimate of this coupling. Furthermore, a morphed intermolecular potential for the vibrationally excited system was also obtained that gives a quantitative estimate of the shift in the potential due to the excitation. The submillimeter analysis is consistent with a ground state having its highest probability as a paired hydrogen bond configuration with R(0) = 4.56372(1) Å and an average angle θ=cos(-1)(<cos(2) θ>(1/2)) = 46.40(1)° (between the diatom center of mass∕center of mass axis and direction of each component hydrogen iodide molecule). On monodeuteration, however, the ground state is predicted to undergo an anomalous structural isotope change to an L-shaped HI-DI structure with highest probability at R(0) = 4.51 Å, θ(1) = 83°, θ(2) = 177°, and φ = 180°. These results provide a test for large scale ab initio calculations and have implications for the interpretation of photoinduced chemistry and other properties of the dimer.