The folding of genomic DNA from the beads-on-a-string like structure of nucleosomes into higher order assemblies is critically linked to nuclear processes. We have calculated the first 3D structures of entire mammalian genomes using data from a new chromosome conformation capture procedure that allows us to first image and then process single cells. This has allowed us to study genome folding down to a scale of <100 kb and to validate the structures. We show that the structures of individual topological-associated domains and loops vary very substantially from cell-to-cell. By contrast, A/B compartments, lamin-associated domains and active enhancers/promoters are organized in a consistent way on a genome-wide basis in every cell, suggesting that they could drive chromosome and genome folding. Through studying pluripotency factor- and NuRD-regulated genes, we illustrate how single cell genome structure determination provides a novel approach for investigating biological processes.