(Parallel-faced hemihedral).
The only elements of symmetry are the triad axis and a centre of symmetry. The general form {hkl} is a rhombohedron, and is a hemihedral form, with parallel faces, of the scalenohedron. The form {hkl}, where h − 2k + l = 0, is also a rhombohedron, being the hemihedral form of the hexagonal bipyramid. The dihexagonal prism {hkl} of the holosymmetric class becomes here a hexagonal prism. The rhombohedra (hkk), hexagonal prisms {211} and {101}, and the basal pinacoid {111} are geometrically the same in this class as in the holosymmetric class.
Fig. 76 represents a crystal of dioptase with the fundamental rhombohedron r {100} and the hexagonal prism of the second order m {101} combined with the rhombohedron s {031}.
Examples of minerals which crystallize in this class are phenacite, dioptase, willemite, dolomite, ilmenite and pyrophanite: amongst artificial substances is ammonium periodate ((NH4)4I2O9·3H2O).
Trigonal Pyramidal Class
(Hemimorphic-tetartohedral).
| Fig. 76.—Crystal of Dioptase. |
Here there is only the triad axis of symmetry, which is uniterminal. The general form {hkl} is a trigonal pyramid consisting of three faces at one end of the crystal. All other forms, in which the faces are neither parallel nor perpendicular to the triad axis, are trigonal pyramids. All the prisms are trigonal prisms; and perpendicular to these are two pedions.
The only substance known to crystallize in this class is sodium periodate (NaIO4·3H2O), the crystals of which are circularly polarizing.
Trigonal Bipyramidal Class