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Teeth segmentation is an important topic in dental restorations that is essential for crown generation, diagnosis, and treatment planning. In the dental field, the variability of input data is high and there are no publicly available 3D dental arch datasets. Although there has been improvement in the field provided by recent deep learning architectures on 3D data, there still exists some problems such as properly identifying missing teeth in an arch. We propose to use spectral clustering as a self-supervisory signal to joint-train neural networks for segmentation of 3D arches. Our approach is motivated by the observation that K-means clustering provides cues to capture margin lines related to human perception. The main idea is to automatically generate training data by decomposing unlabeled 3D arches into segments relying solely on geometric information. The network is then trained using a joint loss that combines a supervised loss of annotated input and a self-supervised loss of non-labeled input. Our collected data has a variety of arches including arches with missing teeth. Our experimental results show improvement over the fully supervised state-of-the-art MeshSegNet when using semi-supervised learning. Finally, we contribute code and a dataset.