Single-view reconstruction (SVR) of the vertebrae is a technique used to reconstruct their 3D surface from a single 2D radiograph. This has great potential to improve Minimally Invasive Spine Surgery (MISS) by providing real-time 3D anatomical context for surgical planning and diagnosis. Despite its potential, SVR for vertebrae remains underexplored due to the inherent challenges of recovering one dimension of missing information from a single 2D view and the lack of open source datasets. To address this, we present a novel SVR architecture, 3D-ReVert, that combines a ResNet-18 encoder with a Dynamic Graph Convolutional Neural Network (DGCNN) decoder to reconstruct the vertebrae mesh from a single Digitally Reconstructed Radiograph (DRR). DGCNNs effectively process non-Euclidean data such as point clouds and meshes by capturing the local geometric information in the feature space, making them well-suited for 3D surface reconstruction. Additionally, to address the lack of readily available data, we introduce an open-source dataset with 11,400 paired DRR–mesh samples with DRRs rendered for 475 unique meshes across 24 diverse viewpoints. We evaluated the results using four different reconstruction metrics, with the model achieving a Dice score of 80.2% and a Hausdorff Distance of 2.06 mm. We also performed an extensive study of six clinically relevant parameters of the predicted 3D surfaces. Our comparative study demonstrates that 3D-ReVert outperforms existing methods that use biplanar DRRs for vertebral surface reconstruction. The implementation of 3D-ReVert and the dataset can be found in this repository: .