Geometrical frustration, a central paradigm in condensed matter physics, provides a unifying language for systems in which locally preferred interactions cannot be made globally compatible. Here, we use this language to formulate a minimal theory of frustrated neural timing, mapping repulsively coupled rhythmic units onto antiferromagnetic XY models. In this formulation, the condensed-matter concepts of local constraints, degenerate ground-state manifolds, metastability, and quench dynamics are used to guide our analysis of structured neural phase dynamics. This paper analyzes a hierarchy of geometries, beginning with a triangle as the minimal frustrated motif with two chiral 120° timing states, then a tetrahedron whose reduced ground-state manifold consists of intersecting continuous branches associated with antipodal pairings, and finally a kagome lattice on which local constraints define a constrained three-coloring manifold. The kagome lattice reveals that zero-temperature relaxation suppresses global synchrony but typically selects low-energy metastable torque-balanced states rather than exact ground states. We then show how the phase theory can be carried back towards biophysical neural models by treating the minimal framework as an effective-interaction target, where geometrical timing frustration arises from preferred phase lags that become incompatible around closed motifs. Our results suggest that weak global coherence in neural systems doesn’t necessarily signal disordered activity, but can instead reflect structured local timing order within a frustrated dynamical landscape.