Here there are the full number of axes of symmetry, but no planes or centre of symmetry. The general form {hkl} is bounded by eight trapezoidal faces and is the tetragonal trapezohedron.
Examples are nickel sulphate (NiSO4·6H2O), guanidine carbonate ((CH5N3)2H2CO3), strychnine sulphate ((C21H22N2O2)2·H2SO4·6H2O).
Bisphenoidal Class
(Bisphenoidal-tetartohedral).
Here there is only a single dyad axis of symmetry, which coincides with the principal axis. All the forms, except the prisms and basal pinacoid, are sphenoids. Crystals possessing this type of symmetry have not yet been observed.
3. ORTHORHOMBIC SYSTEM
(Rhombic; Prismatic; Trimetric).
In this system the three crystallographic axes are all at right angles, but they are of different lengths and not interchangeable. The parameters, or axial ratios, are a : b : c, these referring to the axes OX, OY and OZ respectively. The choice of a vertical axis, OZ = c, is arbitrary, and it is customary to place the longer of the two horizontal axes from left to right (OY = b) and take it as unity: this is called the “macro-axis” or “macro-diagonal” (from μακρός, long), whilst the shorter horizontal axis (OX = a) is called the “brachy-axis” or “brachy-diagonal” (from βραχύς, short). The axial ratios are constant for crystals of any one substance and are characteristic of it; for example, in barytes (BaSO4), a : b : c = 0.8152 : 1 : 1.3136; in anglesite (PbSO4), a : b : c = 0.7852: 1 : 1.2894; in cerussite (PbCO3), a : b : c = 0.6100 : 1 : 0.7230.
There are three symmetry-classes in this system:—