(Plagihedral-hemihedral; Pentagonal icositetrahedral; Gyroidal[4]).
In this class there are the full number of axes of symmetry (three
tetrad, four triad and six dyad), but no planes of symmetry and no
centre of symmetry.
[Illustration: FIG. 40.--Pentagonal Icositetrahedron.]
[Illustration: FIG. 41.--Tetrahedral Pentagonal Dodecahedron.]
Pentagonal icositetrahedron (fig. 40). This is the only simple form in
this class which differs geometrically from those of the holosymmetric
class. By suppressing either one or other set of alternate faces of
the hexakis-octahedron two pentagonal icositetrahedra {hkl} and {khl}
are derived. These are each bounded by twenty-four irregular
pentagons, and although similar to each other they are respectively
right- and left-handed, one being the mirror image of the other; such
similar but nonsuperposable forms are said to be enantiomorphous
([Greek: enantios], opposite, and [Greek: morphe], form), and crystals
showing such forms sometimes rotate the plane of polarization of
plane-polarized light. Faces of a pentagonal icositetrahedron with
high indices have been very rarely observed on crystals of cuprite,
potassium chloride and ammonium chloride, but none of these are
circular polarizing.