# the list of 55 additional points needed to block the difficult coloring of G51
 
 [0, 0, 12, 0], [0, 0, -24, 0], [0, 0, -6, -6], [0, 0, -6, 6], [-18, 0, -6, 0], [-12, 0, -6, -6], [-12, 0, -6, 6], [-6, 0, 12, -6], [-6, 0, 12, 6], [0, 0, 30, 6], [-6, 0, -24, 6], [-32, -6, -12, 2], [-32, 6, -12, -2], [-30, -6, -18, -6], [-30, -6, -12, 0], [-30, -6, 6, 6], [-30, -6, 24, 0], [-30, 0, 12, 6], [-30, 6, -18, 6], [-30, 6, -12, 0], [-30, 6, 6, -6], [-30, 6, 24, 0], [-27, -9, -15, 9], [-27, -9, 3, 3], [-27, -9, 21, -3], [-27, -3, -27, 3], [-27, -3, -3, 3], [-27, 3, -3, -3], [-27, 9, -15, 3], [-27, 9, 3, -3], [-27, 9, 21, 3], [-24, -6, -18, 0], [-24, -6, 24, -6], [-24, 0, -24, 0], [-24, 0, -6, -6], [-24, 0, -6, 6], [-24, 0, 12, 0], [-24, 6, -18, 0], [-24, 18, -6, 0], [-22, -6, -12, 4], [-22, 0, -6, -4], [-22, 0, -6, 4], [-22, 0, 12, -2], [-22, 0, 12, 2], [-21, -9, -15, -9], [-21, -9, -15, 3], [-21, -9, 3, -3], [-21, -9, 21, 3], [-21, -3, -3, -3], [-21, -3, 15, 3], [-21, 3, -9, -3], [-21, 3, -3, 3], [-21, 3, 15, -3], [-21, 9, -15, -3], [-21, 9, -15, 9], [-21, 9, 3, -9], [-21, 9, 3, 3], [-21, 9, 21, -3], [-19, -3, -3, -1], [-19, 3, -3, 1], [-18, -18, 12, 0], [-18, -12, 6, 0], [-18, 0, 12, -6], [-18, 0, 12, 6], [-18, 12, 6, 0], [-18, 18, -6, 6], [-18, 18, 12, 0], [-16, 0, 12, -4], [-16, 0, 12, 4], [-15, -9, 3, 3], [-15, -3, -3, 3], [-15, -3, 9, 3], [-15, 3, -3, -3], [-15, 3, 9, -3], [-15, 9, -15, 3], [-15, 9, 3, 9], [-14, -6, 6, 2], [-14, 0, 12, 2], [-14, 6, 6, -2], [-13, -3, -3, 5], [-12, -6, -12, 6], [-12, -6, 0, -6], [-12, -6, 0, 6], [-12, -6, 6, 0], [-12, 6, 0, -6], [-12, 6, 0, 6], [-12, 6, 6, 0], [-12, 12, 0, 0], [-12, 18, -6, 0], [-9, -9, 3, 9], [-9, -3, -9, 3], [-9, -3, -3, -3], [-9, -3, 9, -3], [-9, 3, -3, 3], [-9, 9, 3, -9], [-9, 15, -3, 3], [-8, -6, 0, -2], [-8, 6, 0, 2], [-6, -12, 6, 0], [-6, -6, 0, 0], [-6, -6, 6, -6], [-6, 0, -6, 12], [-6, 6, 0, 0], [-5, -3, -3, 1], [-5, 3, -3, -1], [-4, -6, 0, 2], [-4, 6, 0, -2], [-3, -3, -3, 3], [-3, 3, -3, 9]