We experimentally probe the coupling between particle shape and long-range interaction,using long-range interacting polygons.For two typical space-filling polygons,square and triangle,we find two types of coupling modes that predominantly control the structure formation.Specifically,the rotational ordering of squares brings a lattice deformation that produces a hexagonal-to-rhombic transition in the high density regime,whereas the alignment of triangles introduces a large geometric frustration that causes an order-to-disorder transition.Moreover,the two coupling modes lead to small and large “internal roughness” of the two systems,and thus predominantly control their structure relaxations.Our study thus provides a physical picture to the coupling between long-range interaction effect and short-range shape effect in the high-density regime unexplored before.