(Bisphenoidal-hemihedral).
Here there are only three dyad axes and two planes of symmetry, the
former coinciding with the crystallographic axes and the latter
bisecting the angles between the horizontal pair. The dyad axis of
symmetry, which in this class coincides with the principal axis of the
crystal, has certain of the characters of a tetrad axis, and is
sometimes called a tetrad axis of "alternating symmetry"; a face on
the upper half of the crystal if rotated through 90 deg. about this
axis and reflected across the equatorial plane falls into the position
of a face on the lower half of the crystal. This kind of symmetry,
with simultaneous rotation about an axis and reflection across a
plane, is also called "composite symmetry."
In this class all except two of the simple forms are geometrically the
same as in the holosymmetric class.
Bisphenoid ([Greek: sphen], a wedge) (fig. 50). This is a double
wedge-shaped solid bounded by four equal isosceles triangles; it has
the indices {111}, {211}, {112}, &c., or in general {hhl}. By
suppressing either one or other set of alternate faces of the
tetragonal bipyramid of the first order (fig. 42) two bisphenoids are
derived, in the same way that two tetrahedra are derived from the
regular octahedron.
Tetragonal scalenohedron or ditetragonal bisphenoid (fig. 51). This is
bounded by eight scalene triangles and has the indices {hkl}. It may
be considered as the hemihedral form of the ditetragonal bipyramid.
[Illustration: FIG. 50.--Tetragonal Bisphenoids.]
[Illustration: FIG. 51.--Tetragonal Scalenohedron.]
The crystal of chalcopyrite (CuFeS2) represented in fig. 52 is a
combination of two bisphenoids (P and P'), two bipyramids of the
second order (b and c), and the basal pinacoid (a). Stannite
(Cu2FeSnS4), acid potassium phosphate (H2KPO4), mercuric cyanide, and
urea (CO(NH2)2) also crystallize in this class.