The 3D morphology of cortical neurons is highly complex with widely varying shapes and has long been used to classify neurons into cell types. Classification based on morphology has classically been done by either laborious expert analysis through visual inspection or by computing a set of predefined features that could be quantitatively measured. Both approaches are prone to bias and subjectivity. The classification of neurons by experts was shown to have a high variance, and becomes infeasible with larger datasets. Similarly, the definition of fixed morphological features for classification introduces biases into the classification process by only taking a limited set of features into account. Large-scale datasets of 3D reconstructions have recently become available, enabling unsupervised machine learning methods. Here, we propose a method to learn relevant features from 3D neuron morphologies in a purely data-driven way. We represent neurons as graphs and use a contrastive learning objective similar to recent methods in computer vision to embed them in a latent space. By doing so, we learn a low dimensional representation of the morphology that captures the essence of the 3D shape and enables clustering into cell types. Our approach allows us to differentiate between spiny and aspiny neurons in the mouse visual cortex and clusters the cells with regard to their cortical layer of origin. Furthermore, when clustering the excitatory neurons in latent space, clusters of different cell types emerge, such as L5 thick tufted pyramid cells and stellate cells. We compare our approach to clustering based on expert-defined features and show better predictability of our clusters as well as qualitatively more uniform clusters. Overall, our results suggest that unsupervised representations of 3D morphologies can be learned in a data-driven fashion and could potentially be used to discover novel neuronal cell types.