Pyramidal Class
(Hemimorphic-tetartohedral).
Here the only element of symmetry is the tetrad axis. The pyramids of the first {hhl}, second {hol} and third {hkl} orders have each only four faces at one or other end of the crystal, and are hemimorphic. All the simple forms are thus open forms.
Examples are wulfenite (PbMoO4) and barium antimonyl dextro-tartrate (Ba(SbO)2(C4H4O6)·H2O).
Ditetragonal Pyramidal Class
(Hemimorphic-hemihedral).
Here there are two pairs of vertical planes of symmetry intersecting in the tetrad axis. The pyramids {hhl} and {hol} and the bipyramid {hkl} are all hemimorphic.
Examples are iodosuccimide (C4H4O2NI), silver fluoride (AgF·H2O), and penta-erythrite (C5H12O4). No examples are known amongst minerals.
Trapezohedral Class
(Trapezohedral-hemihedral).