We studied the 3D structural organization of the fission yeast genome, which emerges from the tethering of heterochromatic regions in otherwise randomly configured chromosomes represented as flexible polymer chains in an nuclear environment. This model is sufficient to explain in a statistical manner many experimentally determined distinctive features of the fission yeast genome, including chromatin interaction patterns from Hi-C experiments and the co-locations of functionally related and co-expressed genes, such as genes expressed by Pol-III. Our findings demonstrate that some previously described structure-function correlations can be explained as a consequence of random chromatin collisions driven by a few geometric constraints (mainly due to centromere-SPB and telomere-NE tethering) combined with the specific gene locations in the chromosome sequence. We also performed a comparative analysis between the fission and budding yeast genome structures, for which we previously detected a similar organizing principle. However, due to the different chromosome sizes and numbers, substantial differences are observed in the 3D structural genome organization between the two species, most notably in the nuclear locations of orthologous genes, and the extent of nuclear territories for genes and chromosomes. However, despite those differences, remarkably, functional similarities are maintained, which is evident when comparing spatial clustering of functionally related genes in both yeasts. Functionally related genes show a similar spatial clustering behavior in both yeasts, even though their nuclear locations are largely different between the yeast species. 