This paper presents a combinatorial algorithm for reconstructing a smooth surface from a finite set of sample points in three-dimensional space. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation, ensuring that the output is topologically valid and converges to the original surface in both pointwise and surface normal terms. The authors prove the correctness of the algorithm by demonstrating that for densely sampled surfaces, the output is topologically valid and converges to the original surface. The paper includes an implementation of the algorithm and showcases example outputs. The algorithm relies on the Delaunay triangulation and Voronoi diagram, extending previous work on curve reconstruction in two dimensions. The authors discuss the theoretical guarantees of the algorithm, including the conditions under which it works correctly, and provide proofs for these guarantees. The paper also addresses practical aspects such as handling degeneracies and near degeneracies, and discusses potential future work, including generalizations to higher dimensions and applications in manifold learning.This paper presents a combinatorial algorithm for reconstructing a smooth surface from a finite set of sample points in three-dimensional space. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation, ensuring that the output is topologically valid and converges to the original surface in both pointwise and surface normal terms. The authors prove the correctness of the algorithm by demonstrating that for densely sampled surfaces, the output is topologically valid and converges to the original surface. The paper includes an implementation of the algorithm and showcases example outputs. The algorithm relies on the Delaunay triangulation and Voronoi diagram, extending previous work on curve reconstruction in two dimensions. The authors discuss the theoretical guarantees of the algorithm, including the conditions under which it works correctly, and provide proofs for these guarantees. The paper also addresses practical aspects such as handling degeneracies and near degeneracies, and discusses potential future work, including generalizations to higher dimensions and applications in manifold learning.