The dynamic three-dimensional chromatin architecture of genomes and its co-evolutionary connection to its function - the storage, expression, and replication of genetic information - is still one of the central issues in biology. Here, we describe the much debated 3D-architecture of the human and mouse genomes from the nucleosomal to the megabase pair level by a novel approach combining selective high-throughput high-resolution chromosomal interaction capture (T2C), polymer simulations, and scaling analysis of the 3D-architecture and the DNA sequence: The genome is compacted into a chromatin quasi-fibre with ~5+-1 nucleosomes/11nm, folded into stable ~30-100 kbp loops forming stable loop aggregates/rosettes connected by similar sized linkers. Minor but significant variations in the architecture are seen between cell types/functional states. The architecture and the DNA sequence show very similar fine-structured multi-scaling behaviour confirming their co-evolution and the above. This architecture, its dynamics, and accessibility balance stability and flexibility ensuring genome integrity and variation enabling gene expression/regulation by self-organization of (in)active units already in proximity. Our results agree with the heuristics of the field and allow "architectural sequencing" at a genome mechanics level to understand the inseparable systems genomic properties.