Non-homologous chromosomal contacts (NHCCs) between different chromosomes participate considerably in gene and genome regulation. However, due to analytical challenges, NHCCs are currently considered as singular, stochastic events, and their extent and fundamental principles across cell types and sexes remain controversial. To determine the fundamental properties of NHCCs, we developed a supervised and unsupervised learning algorithm, termed Signature. Signature revealed 40,282 NHCCs and their properties across 62 Hi-C datasets of 53 diploid human cell types. Genomic regions of NHCCs are gene-dense, highly expressed, and harbor genes for cell-specific and sex-specific functions. Extensive inter-telomeric and inter-centromeric clustering occurs across cell types and 61 NHCCs are consistently found at the nuclear speckles. These constitutive ‘anchor loci’ facilitate an axis of genome activity whilst cell-type-specific NHCCs act in discrete hubs. Our results suggest that non-random chromosome positioning is supported by constitutive NHCCs that shape genome topology along an off-centered spatial gradient of genome activity. Overall design: Omni-C datasets of chondrogenic differentiation, CHLA-9, TC-32, and TeloHAEC cells. Each dataset is derived from two biological replicates, each with three technical replicates. Omni-C libraries were sequenced as paired-end runs with 2x150 bp on S4 flowcells of NovaSeq6000 with > 2 billion reads per sample.