We have undertaken a comprehensive spectroscopic survey of the Horologium-Reticulum supercluster (HRS) of galaxies. With a concentration on the intercluster regions, our goal is to resolve the "cosmic web" of filaments, voids, and sheets within the HRS and to examine the interrelationship between them. What are the constituents of the HRS? What can be understood about the formation of such a behemoth from these current constituents? More locally, are there small-scale imprints of the larger, surrounding environment, and can we relate the two with any confidence? What is the relationship between the HRS and the other superclusters in the nearby universe? These are the questions driving our inquiry. To answer them, we have obtained over 2500 galaxy redshifts in the direction of the intercluster regions in the HRS. Specifically, we have developed a sample of galaxies with a limiting brightness of betaJ < 17.5, which samples the galaxy luminosity function down to one magnitude below M? at the mean redshift of the HRS, z is approximately equal to 0.06. Exclusively, these intercluster redshifts were obtained with the six-degree field (6dF), multi-fiber spectrograph at the Anglo-Australian Observatory. In conjunction with the wide-field, 1.2m UK Schmidt, 6dF is the ideal supercluster observatory. Because it deploys the 150 fiber buttons over a 6-degree field, we are able to obtain coherent information over large areas of the sky, as is the case with a supercluster. In addition, we have obtained a complete sample of mean cluster redshifts and velocity dispersions for Abell clusters in the HRS using the Australian National University/2.3m, primarily. For most of the clusters, more than 10 galaxies were observed, and a reliable mean cluster redshift is determined. Furthermore, we have a near complete sample of bJ < 18.6 galaxies over a 4 degree × 4 degree region that encompasses several HRS clusters. With these datasets, we are able to "piece" together various structures over a large range of scales. We have also obtained high-resolution radio imaging over much of this smaller area. We find six void structures in the region with 10 less than or equal to RVOID less than or equal to 15 h-1 Mpc that are completely absent of 6dF galaxies (except for one void that contains a single galaxy down to our observational limits). To discover the voids, we implement the GyVe software tool that provides a 3-D, interactive visualization environment. Furthermore, four of these voids are embedded within the supercluster environment, while the other two are located at the observed boundaries of the HRS. This is reflected in the intrinsically different galaxy number counts profiles as a function of radius. The voids maintain their distinct profiles despite the fact that the 6dF sample is augmented with thousands of previously published redshifts. We also observe that matter (galaxies and clusters) is not distributed evenly around these voids, but seems to follow a highly ordered arrangement. Lastly, the intercluster regions (5-10 h-1 Mpc) within one of the most dense HRS volumes are examined. We define three different intercluster extensions varying in over-density from 20-60, which is 7-10 times the adjacent control volumes. Furthermore, we calculate a velocity dispersion of approximately 350 kms-1 within one intercluster filament approximately 11 h-1 Mpc in projected length. While varying in projected spatial width, the extended collection of intercluster galaxies joins the two richest complexes in the region. These galaxies also exhibit a preferred orientation of 60-90 degrees along its length. We further note that while some preferred orientations are found within smaller substructures, e.g., galaxy groups, these characterizations do not match the larger-scale galaxy distributions.