International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 
International Tables for Crystallography (2016). Vol. A, ch. 3.2, p. 734

^{†}The Hermann–Mauguin symbols of the two icosahedral point groups are often written as 532 and (see text).
^{‡}Rotating and `antirotating' forms in the cylindrical system have no `vertical' mirror planes, whereas stationary forms have infinitely many vertical mirror planes. In classes ∞ and , enantiomorphism occurs, i.e. forms with opposite senses of rotation. Class exhibits no enantiomorphism due to the centre of symmetry, even though the double cone is rotating in one direction. This can be understood as follows: The handedness of a rotating cone depends on the sense of rotation with respect to the axial direction from the base to the tip of the cone. Thus, the rotating double cone consists of two cones with opposite handedness and opposite orientations related by the (single) horizontal mirror plane. In contrast, the `antirotating' double cone in class consists of two cones of equal handedness and opposite orientations, which are related by the (infinitely many) twofold axes. The term `antirotating' means that upper and lower halves of the forms rotate in opposite directions. ^{§}The spheres in class of the spherical system must rotate around an axis with at least two different orientations, in order to suppress all mirror planes. This class exhibits enantiomorphism, i.e. it contains spheres with either righthanded or lefthanded senses of rotation around the axes (cf. Section 3.2.2.4, Optical properties). The stationary spheres in class contain infinitely many mirror planes through the centres of the spheres. Group is sometimes symbolized by ; group by or . The symbols used here indicate the minimal symmetry necessary to generate the groups; they show, furthermore, the relation to the cubic groups. The Schoenflies symbol K is derived from the German name Kugelgruppe. 