Conditions for grid points to be simple on the body-centered cubic (bcc) grid are presented and proved to be correct. For a skeletonization algorithm to be topology-preserving, the concept of simple points is important. We prove that deletion of simple points, according to our definition, on the bcc grid preserves topology. This characterization has been used in a previous paper describing a skeletonization algorithm on the face-centered cubic and the bcc grids. The characterization is also used to prove the correctness of conditions for removing grid points in parallel on the bcc grid.