(Trapezohedral-hemihedral).
Here there are three similar dyad axes inclined to one another at 60
deg. and perpendicular to the triad axis. There are no planes or
centre of symmetry. The dyad axes are uniterminal, and are
pyro-electric axes. Crystals of most substances of this class rotate
the plane of polarization of a beam of light.
FIG. 74.--Trigonal Trapezohedron.
FIG. 75.--Trigonal Bipyramid.
In this class the rhombohedra {hkk}, the hexagonal prism {21'1'}, and
the basal pinacoid {111} are geometrically the same as in the
holosymmetric class; the trigonal prism {101'} and the ditrigonal
prisms are as in the ditrigonal pyramidal class. The remaining simple
forms are:--
Trigonal trapezohedron (fig. 74), bounded by six trapezoidal faces.
There are two complementary and enantiomorphous trapezohedra, {hkl}
and {hlk}, derivable from the scalenohedron.
Trigonal bipyramid (fig. 75), bounded by six isosceles triangles; the
indices are {hkl}, where h - 2k + l = 0, as in the hexagonal
bipyramid.
The only minerals crystallizing in this class are quartz (q.v.) and
cinnabar, both of which rotate the plane of a beam of polarized light
transmitted along the triad axis. Other examples are dithionates of
lead (PbS2O6.4H2O), calcium and strontium, and of potassium (K2S2O6),
benzil, matico-stearoptene.