TRIGONAL

BIPYRAMIDAL  CLASS Here there is a plane of symmetry perpendicular to the triad axis . The trigonal pyramids of the last class are here trigonal bipyramids (fig . 75) ; the prisms are all trigonal prisms, and parallel to the plane of symmetry is the basal pinacoid . No example is known for this class . Dioptase . Here there are three similar planes of sym- metry 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, pp}, (hid) for faces above the equatorial plane of symmetry and (pr) for faces below: with hexagonal axes there would be only one set of indices . The hexagonal bipyramids, the hexagonal prism 1103} and the basal pinacoid 1111} are geometrically the same in this class as in the holosymmetric class . The trigonal prism 12YYj and ditrigonal prisms fall are the same as in the ditrigonal pyramidal class . The only representative of this type of symmetry is the mineral benitoite (q.v.) . Hexagonal Division .

In crystals of this division of the hexa- FIG.77.—Dihexagonal gonal

system the principal axis is a hexad Bipyramid . 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 .