Atomic systems (molecules, crystals, proteins, nanoclusters, etc.) are naturally represented by a set of coordinates in 3D space labeled by atom type. This is a challenging representation to use for neural networks because the coordinates are sensitive to 3D rotations and translations and there is no canonical orientation or position for these systems. Overcoming these challenges. we present an autoencoder that is able to encode atomic geometries represented as points into a feature vector and decode that feature vector back to the original geometry. This autoencoder, built from Euclidean Neural Networks, is equivariant to 3D rotations and translations at every layer and is thus able to encode geometric motifs in any orientation or location after seeing only one example. In this talk, we describe the autoencoder design and demonstrate its capabilities on a variety of geometric examples and chemical datasets.