Symmetry is crucial for understanding structural patterns and supports tasks such as object recognition and scene understanding. This paper focuses on rotational symmetry, where objects remain unchanged when rotated around a central axis, requiring the detection of rotation centers and supporting vertices. Traditional methods relied on hand-crafted feature matching for identifying rotation centers and vertices, while recent approaches use convolutional neural networks (CNNs) as segmentation models for rotation center detection. However, 2D-based models struggle to preserve 3D geometric properties due to distortions caused by viewpoint variation. To address this, we propose a rotation symmetry detection model that directly predicts rotation centers and vertices in 3D space, projecting the results back to 2D while maintaining structural consistency. By incorporating a vertex reconstruction stage that enforces 3D geometric priors—such as equal side lengths and interior angles for regular polygons—our model achieves greater robustness and geometric accuracy. Experiments on DENDI dataset show that our approach outperforms previous state-of-the-art methods in rotation center detection and demonstrates the effectiveness of 3D geometric priors through ablation studies on vertex reconstruction.