Equidistance between primary sensory-motor landmarks shapes functional specialisation in the human brain

The human cortex is organized around primary sensory-motor landmarks, but the way these distances shape large-scale functional organization remains unclear. Using geodesic measures in males and females, we show that global minimum distance to sensory-motor landmarks aligns with the principal gradient of intrinsic connectivity, reflecting the shift from unimodal to heteromodal cortex, while equidistance between landmarks captures complementary organizational patterns. Heteromodal networks, including default mode, control, and limbic systems, occupy cortical regions that are both distant from primary systems and relatively balanced between them. Subsystems within these networks exhibit distinctive spatial embeddings: core default mode regions sit equidistant between visual and somatomotor cortex, frontotemporal default mode regions favour auditory cortex but remain relatively balanced, and medial temporal regions are biased toward visual cortex. Control network subsystems also vary: the control-DMN subsystem occupies the most distant and equidistant positions, core control is closer to motor regions, and medial control is closer to visual cortex, reflecting their different functional specializations. At the parcel level, greater equidistance predicts stronger task-evoked activation, particularly in heteromodal border zones. These findings highlight two complementary spatial principles -- proximity and balance -- that structure the cortex, shaping both the location and functional profile of heteromodal networks.Significance statement Distance from unimodal cortex has been proposed as a structural constraint on functional organisation. However, it remains unclear how relative position with respect to multiple sensory-motor landmarks contributes to functional specialisation. Here, we show that both absolute distance from primary landmarks and their relative balance (equidistance) shape the organisation of heteromodal networks. Equidistance between specific sensory-motor landmarks differentiates heteromodal subsystems and predicts task-evoked activation during story comprehension and mathematical reasoning. These results demonstrate that cortical geometry is linked to cognitive function, and highlight two complementary spatial principles - proximity and balance - that structure the cortex and shape the functional profile of heteromodal networks.