The locations of proteins and epigenetic marks on the chromosomal DNA sequence are believed to demarcate the eukaryotic genome into distinct structural and functional domains that contribute to gene regulation and genome organization. However, how these proteins and epigenetic marks are organized in three dimensions remains unknown. Recent advances in proximity-ligation methodologies and high resolution microscopy have begun to expand our understanding of these spatial relationships. Here we use polymer models to examine the spatial organization of epigenetic marks, euchromatin and heterochromatin, and origins of replication within the Schizosaccharomyces pombe genome. These models incorporate data from microscopy and proximity-ligation experiments that inform on the positions of certain elements and contacts within and between chromosomes. Our results show a striking degree of compartmentalization of epigenetic and genomic features and lead to the proposal of a diffusion based mechanism, centred on the spindle pole body, for the coordination of DNA replication in S. pombe.