A computational study of gaseous helium-3 at T = 5.23 K, for number densities rho(N) < 0.0021 angstrom(-3), analyzing the different pair and triplet structures in both the r and the k spaces, is presented. Structures in r space (i.e., instantaneous, total continuous linear response, and centroids) are determined via path-integral Monte Carlo simulations in the canonical ensemble by utilizing the Aziz-Slaman and the SAPT2 interatomic potentials. Additional results obtained with the application of two closures for triplets in r space, the Kirkwood superposition approximation and the Jackson-Feenberg convolution, are also reported. Besides, an analysis of the nonsuitability of quantum hard spheres for describing this system is included. The pair structures in k space are fixed via Ornstein-Zernike schemes appropriate for dealing with quantum diffraction effects in fluids. The effect on the quality of the computed isothermal compressibilities brought about by increasing the sample size in the simulations and by the subsequent application of a grand ensemble correction to the asymptotic behavior of the canonical pair radial correlation functions is also investigated. Furthermore, it is demonstrated analytically that the methods of classical statistical mechanics for dealing with the higher-order direct correlation functions remain fully valid for studying the higher-order correlations of path-integral centroids. By taking advantage of this result, the triplet structure factors for the centroid (also for the instantaneous) correlations are computed by following a number of distinct Closures and methods that involve triplet direct con-elation functions. The latter computations are intended to explore an alternative scheme to the very expensive fixing of triplet structure factors through direct path integral Simulations, an alternative which is expected to yield the main features of these triplet quantities for this gas. Comparison with experiment is made wherever possible, and the results presented allow one to explain the substantial structural features existing in gaseous helium-3.