Description
Complex two-dimensional lattices with mixed rotational symmetries provide a versatile platform for emergent mechanical, photonic, and electronic responses, yet their realization is often limited by the geometric frustration associated with competing local symmetries. Conventional approaches impose the target structure through particle anisotropy, directional bonding, or external templates, which strongly constrain the configurational degrees of freedom and can trap defects far from equilibrium. Here we introduce a dual-symmetry-guided (DSG) principle that controls complex order through a sparse symmetry-encoded external potential. By decomposing a target tiling into two mutually dual sublattices and pinning only one of them with optical traps, the remaining mobile particles experience an effective geometric field and relax, through isotropic repulsive interactions, into the complementary sublattice required to recover the full structure. We experimentally realize a series of Archimedean lattices and extend the same principle to two-dimensional quasicrystalline order, in quantitative agreement with simulations. Analysis of the particle configurations shows that sparse dual pinning preserves connected free volume, allows defect motion and annihilation, and lowers kinetic barriers relative to full templating. These results demonstrate that complex symmetry can be encoded by a minimal subset of dual geometric constraints, providing a physically transparent mechanism for stabilizing complex lattices with isotropic interactions.
