#N Moore: [(0, -1), (1, -1), (1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0), (-1, -1)]
#S rotate2: [[(1, 5), (2, 6), (3, 7), (4, 8)]]
#S rotate2reflect: [[(1, 5), (2, 6), (3, 7), (4, 8)], [(2, 8), (3, 7), (4, 6)]]
#S rotate4: [[(1, 3, 5, 7), (2, 4, 6, 8)]]
#S rotate4reflect: [[(1, 3, 5, 7), (2, 4, 6, 8)], [(2, 8), (3, 7), (4, 6)]]
#S rotate8: [[(1, 2, 3, 4, 5, 6, 7, 8)]]
#S rotate8reflect: [[(1, 2, 3, 4, 5, 6, 7, 8)], [(2, 8), (3, 7), (4, 6)]]
#S reflect_horizontal: [[(2, 8), (3, 7), (4, 6)]]

#N vonNeumann: [(0, -1), (1, 0), (0, 1), (-1, 0)]
#S rotate2: [[(1, 3), (2, 4)]]
#S rotate2reflect: [[(1, 3)], [(2, 4)]]
#S rotate4: [[(1, 2, 3, 4)]]
#S rotate4reflect: [[(1, 2, 3, 4)], [(2, 4)]]
#S reflect_horizontal: [[(2, 4)]]

#N hexagonal: [(0, -1), (1, 0), (1, 1), (0, 1), (-1, 0), (-1, -1)]
#S rotate2: [[(1, 4), (2, 5), (3, 6)]]
#S rotate3: [[(1, 3, 5), (2, 4, 6)]]
#S rotate6: [[(1, 2, 3, 4, 5, 6)]]
#S rotate6reflect: [[(1, 2, 3, 4, 5, 6)], [(1, 6), (2, 5), (3, 4)]]
#S reflect_horizontal: [[(1, 6), (2, 5), (3, 4)]]

#N oneDimensional: [(-1, 0), (1, 0)]
#S reflect: [[(1, 2)]]

#N 2: [(-1, 0), (1, 0)]
#N 4: [(0, -1), (-1, 0), (1, 0), (0, 1)]
#N 6: [(0, -1), (1, 0), (1, 1), (0, 1), (-1, 0), (-1, -1)]
#N 8: [(-1, -1), (1, -1), (-1, 1), (1, 1), (0, -1), (-1, 0), (1, 0), (0, 1)]