There exists a bewildering variety of notations for the thirty-two classes of crystal-symmetry and for the 230 groups of symmetry-movements which control the arrangements of atoms building up a crystalline medium. The notation which has found most favour has been that of Schoenflies's ' Krystallsysteme und Krystallstructur ' (1891). This was followed in Hilton's ' Mathematical Crystallography ' (1903) (see the second column of the table given below), and more recently in Niggli's 'Geometrische Kristallographie des Diskontinuums' (1919).