(Hemihedral).
Here there are three dyad axes, but no planes of symmetry and no centre of symmetry. The general form {hkl} is a bisphenoid (fig. 61) bounded by four scalene triangles. The other simple forms are geometrically the same as in the holosymmetric class.
Examples: epsomite (Epsom salts, MgSO4·7H2O), goslarite (ZnSO4·7H2O), silver nitrate, sodium potassium dextro-tartrate (seignette salt, NaKC4H4O6·4H2O), potassium antimonyl dextro-tartrate (tartar-emetic, K(SbO)C4H4O6), and asparagine (C4H8N2O8·H2O).
4. MONOCLINIC[5] SYSTEM
(Oblique; Monosymmetric).
In this system two of the angles between the crystallographic axes are right angles, but the third angle is oblique, and the axes are of unequal lengths. The axis which is perpendicular to the other two is taken as OY = b (fig. 62) and is called the ortho-axis or ortho-diagonal. The choice of the other two axes is arbitrary; the vertical axis (OZ = c) is usually taken parallel to the edges of a prominently developed prismatic zone, and the clino-axis or clino-diagonal (OX = a) parallel to the zone-axis of some other prominent zone on the crystal. The acute angle between the axes OX and OZ is usually denoted as β, and it is necessary to know its magnitude, in addition to the axial ratios a : b : c, before the crystal is completely determined. As in other systems, except the cubic, these elements, a : b : c and β, are characteristic of the substance. Thus for gypsum a : b : c = 0.6899 : 1 : 0.4124; β = 80° 42′; for orthoclase a : b : c = 0.6585 : 1 : 0.5554; β = 63° 57′; and for cane-sugar a : b : c = 1.2595 : 1 : 0.8782; β = 76° 30′.
Holosymmetric Class
(Holohedral; Prismatic).
Here there is a single plane of symmetry perpendicular to which is a dyad axis; there is also a centre of symmetry. The dyad axis coincides with the ortho-axis OY, and the vertical axis OZ and the clino-axis OX lie in the plane of symmetry.