1AbstractTranscriptional enhancers usually, but not always, regulate genes within the same topologically associating domain (TAD). We hypothesize that this incomplete insulation is due to three-dimensional (3D) structures of TADs: Whereas enhancers and genes buried inside the “core” of a TAD interact mostly with other genomic regions in the same TAD, those on the “surface” can more easily interact with regions outside the TAD. Here we show that a simple measure, the intra-TAD ratio, can quantify the “coreness” of a genomic region with respect to the TAD that it resides in. We further show that TAD surfaces are permissive for high gene expression, and accordingly cell type-specific active cis-regulatory elements (CREs), active histone marks, and transcription factor binding sites are enriched on TAD surfaces, most strongly in chromatin subcompartments typically considered inactive. These findings suggest a “TAD surface CRE” model of gene regulation. In addition, we also find that disease-associated non-coding variants are enriched on TAD surfaces.