How does the brain integrate multiple sources of information to support normal sensorimotor and cognitive functions? To investigate this question we present an overall brain architecture (called "the dual intertwined rings architecture") that relates the functional specialization of cortical networks to their spatial distribution over the cerebral cortex (or "corticotopy"). Recent results suggest that the resting state networks (RSNs) are organized into two large families: 1) a sensorimotor family that includes visual, somatic, and auditory areas and 2) a large association family that comprises parietal, temporal, and frontal regions and also includes the default mode network. We used two large databases of resting state fMRI data, from which we extracted 32 robust RSNs. We estimated: (1) the RSN functional roles by using a projection of the results on task based networks (TBNs) as referenced in large databases of fMRI activation studies; and (2) relationship of the RSNs with the Brodmann Areas. In both classifications, the 32 RSNs are organized into a remarkable architecture of two intertwined rings per hemisphere and so four rings linked by homotopic connections. The first ring forms a continuous ensemble and includes visual, somatic, and auditory cortices, with interspersed bimodal cortices (auditory-visual, visual-somatic and auditory-somatic, abbreviated as VSA ring). The second ring integrates distant parietal, temporal and frontal regions (PTF ring) through a network of association fiber tracts which closes the ring anatomically and ensures a functional continuity within the ring. The PTF ring relates association cortices specialized in attention, language and working memory, to the networks involved in motivation and biological regulation and rhythms. This "dual intertwined architecture" suggests a dual integrative process: the VSA ring performs fast real-time multimodal integration of sensorimotor information whereas the PTF ring performs multi-temporal integration (i.e., relates past, present, and future representations at different temporal scales).