||Seen as approximations of the Euclidean distance, the city block and chessboard distances in the two-dimensional square grid constitute very rough approximations of the Euclidean distance. The Euclidean distance is better approximated by mixing the city block and chessboard distances, i.e. by allowing 8-neighbours for some local steps when finding the shortest path. Such distances (distances generated by neighbourhood sequences) are defined for the face-centered cubic (fcc) and the body-centered cubic (bcc) grids. Formulas for computing the distances are used to calculate the neighbourhood sequences that best approximate the Euclidean distance.