Point-based geometric representations such as point clouds and Gaussian Splatting are fundamental for 3D understanding. However, the inherent irregularity and high-dimensional nature of point structures present significant challenges for direct 3D learning approaches, which often struggle with scalability and achieve suboptimal performance due to sparse data distributions. In contrast, 2D learning paradigms benefit from well-established architectures with superior optimization stability and efficiency. To bridge this gap, we propose Maniflat3D, a unified framework that systematically transforms volumetric point-based geometries into structured 2D representations through a two-stage process: a multilayer Ball-Pivoting reconstruction with adaptive density control, followed by Scalable Locally Injective Mapping (SLIM) to produce distortion-minimized, bijective UV parameterizations. Our approach explicitly encodes both geometric and attribute information into the flattened domain, enabling conventional 2D neural networks to effectively learn from complex 3D structures such as Gaussian Splatting. Experiments on the ShapeSplat dataset demonstrate that Maniflat3D achieves comparable performance while reducing parameter count by 90\% compared to native 3D baselines, and simultaneously attains 21× compression ratio through neural encoding. These results establish a new paradigm for efficient geometric understanding, demonstrating successful transfer of planar learning advantages to challenging 3D manifold problems through dimensional reduction.