Connectomics is a subfield of neuroscience that aims to map the brains intricate wiring diagram. Accurate neuron segmentation from microscopy volumes is essential for automating connectome reconstruction. However, current state-of-the-art algorithms use image-based convolutional neural networks that are limited to local neuron shape context. Thus, we introduce a new framework that reasons over global neuron shape with a novel point affinity transformer. Our framework embeds a (multi-)neuron point cloud into a fixed-length feature set from which we can decode any point pair affinities, enabling clustering neuron point clouds for automatic proofreading. We also show that the learned feature set can easily be mapped to a contrastive embedding space that enables neuron type classification using a simple KNN classifier. Our approach excels in two demanding connectomics tasks: proofreading segmentation errors and classifying neuron types. Evaluated on three benchmark datasets derived from state-of-the-art connectomes, our method outperforms point transformers, graph neural networks, and unsupervised clustering baselines.