<p>Graph representations of solid state materials that encode only interatomic-distance information lack geometrical resolution, resulting in degenerate representations that may map distinct structures to equivalent graphs. Here, we propose a hypergraph representation scheme for materials that allows for the association of higher-order geometrical information with hyperedges. Hyperedges generalize edges to connected sets of more than two nodes, and may be used to represent triplets and local environments of atoms in materials. This generalization of edges requires a different approach in graph convolution, which is developed in this work. These crystal hypergraph convolutional networks are trained based on various property prediction tasks for a vast set of solid-state materials available via MatBench. Results presented here focus on the improved performance of models based on both pair-wise edges and local environment hyperedges. These results demonstrate that hypergraphs are an effective and efficient method for incorporating geometrical information in material representations.</p>