  Geometric frustration arises when lattice structure prevents simultaneous
minimization of local interactions. It leads to highly degenerate ground states
and, subsequently, complex phases of matter such as water ice, spin ice and
frustrated magnetic materials. Here we report a simple geometrically frustrated
system composed of closely packed colloidal spheres confined between parallel
walls. Diameter-tunable microgel spheres are self-assembled into a buckled
triangular lattice with either up or down displacements analogous to an
antiferromagnetic Ising model on a triangular lattice. Experiment and theory
reveal single-particle dynamics governed by in-plane lattice distortions that
partially relieve frustration and produce ground-states with zigzagging stripes
and subextensive entropy, rather than the more random configurations and
extensive entropy of the antiferromagnetic Ising model. This tunable soft
matter system provides an uncharted arena in which the dynamics of frustration,
thermal excitations and defects can be directly visualized.
