Unlike image or text domains that benefit from an abundance of large-scale datasets, point cloud learning techniques frequently encounter limitations due to the scarcity of extensive datasets. To overcome this limitation, we present Symmetria, a formula-driven dataset that can be generated at any arbitrary scale. By construction, it ensures the absolute availability of precise ground truth, promotes data-efficient experimentation by requiring fewer samples, enables broad generalization across diverse geometric settings, and offers easy extensibility to new tasks and modalities. Using the concept of symmetry, we create shapes with known structure and high variability, enabling neural networks to learn point cloud features effectively. Our results demonstrate that this dataset is highly effective for point cloud self-supervised pre-training, yielding models with strong performance in downstream tasks such as classification and segmentation, which also show good few-shot learning capabilities. Additionally, our dataset can support fine-tuning models to classify real-world objects, highlighting our approach's practical utility and application. We also introduce a challenging task for symmetry detection and provide a benchmark for baseline comparisons. A significant advantage of our approach is the public availability of the dataset, the accompanying code, and the ability to generate very large collections, promoting further research and innovation in point cloud learning.