Buckled monolayers of diameter-tunable microgel spheres constitute a soft-matter model system for studying geometric frustration in hard-condensed-matter antiferromagnetic materials. In the plane, the spheres self-assemble to form a triangular lattice. By considering the free volume available to two spheres slightly out of the plane, one finds an effective antiferromagnetic interaction; each pair of neighboring spheres prefers to be one up and one down. However, the topology of the triangular lattice prevents all pairs from simultaneously satisfying this rule. The micrometer length scale of the spheres enables direct visualization of the ‘spin’ dynamics at the single-particle level. These dynamics exhibit glassiness, which originates from the in-plane lattice distortions that partially relieve frustration and produce ground states with zigzagging stripes.