Here there are three similar planes of symmetry intersecting in the
triad axis, and perpendicular to them is a fourth plane of symmetry;
at the intersection of the three vertical planes with the horizontal
plane are three similar dyad axes; there is no centre of symmetry.
The general form is bounded by twelve scalene triangles and is a
ditrigonal bipyramid. Like the general form of the last class, this
has two sets of indices {hkl, p'q'r'}, (hkl) for faces above the
equatorial plane of symmetry and (p'q'r') for faces below: with
hexagonal axes there would be only one set of indices. The hexagonal
bipyramids, the hexagonal prism {101'} and the basal pinacoid {111}
are geometrically the same in this class as in the holosymmetric
class. The trigonal prism {21'1'} and ditrigonal prisms {hkl} are the
same as in the ditrigonal pyramidal class.
The only representative of this type of symmetry is the mineral
benitoite (q.v.).
[Illustration: FIG. 77.--Dihexagonal Bipyramid.]
_Hexagonal Division._
In crystals of this division of the hexagonal system the principal
axis is a hexad axis of symmetry. Hexagonal axes of reference are
used: if rhombohedral axes be used many of the simple forms will have
two sets of indices.