Animal genomes are organized into chromosomes that are remarkably conserved in their gene content, forming distinct evolutionary units (macrosynteny). We developed a novel three-dimensional chromosomal modelling approach to show that syntenic signals are reflected in conserved three-dimensional networks, encompassed within interaction spheres. We show evidence for evolutionary constraints that could not be surmised by genomic sequence alone, thereby underlining the importance of three-, rather than just two-, dimensional organization.