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Geometric frustration and the ice rule are two concepts that are intimatelyconnected and widespread across condensed matter. The first refers to theinability of a system to satisfy competing interactions in the presence ofspatial constraints. The second, in its more general sense, represents aprescription for the minimization of the topological charges in a constrainedsystem. Both can lead to manifolds of high susceptibility and non-trivial,constrained disorder where exotic behaviors can appear and even be designeddeliberately. In this Colloquium, we describe the emergence of geometricfrustration and the ice rule in soft condensed matter. This Review excludes theextensive developments of mathematical physics within the field of geometricfrustration, but rather focuses on systems of confined micro- or mesoscopicparticles that emerge as a novel paradigm exhibiting spin degrees of freedom.In such systems, geometric frustration can be engineered artificially bycontrolling the spatial topology and geometry of the lattice, the position ofthe individual particle units, or their relative filling fraction. Thesecapabilities enable the creation of novel and exotic phases of matter, and alsopotentially lead towards technological applications related to memory and logicdevices that are based on the motion of topological defects. We review therapid progress in theory and experiments and discuss the intimate physicalconnections with other frustrated systems at different length scales.

Ice Rule and Emergent Frustration in Particle Ice and Beyond