In this class all except two of the simple forms are geometrically the same as in the holosymmetric class.
Bisphenoid (σφήν, a wedge) (fig. 50). This is a double wedge-shaped solid bounded by four equal isosceles triangles; it has the indices {111}, {211}, {112}, &c., or in general {hhl}. By suppressing either one or other set of alternate faces of the tetragonal bipyramid of the first order (fig. 42) two bisphenoids are derived, in the same way that two tetrahedra are derived from the regular octahedron.
Tetragonal scalenohedron or ditetragonal bisphenoid (fig. 51). This is bounded by eight scalene triangles and has the indices {hkl}. It may be considered as the hemihedral form of the ditetragonal bipyramid.
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| Fig. 50.—Tetragonal Bisphenoids. | Fig. 51.—Tetragonal Scalenohedron. |
The crystal of chalcopyrite (CuFeS2) represented in fig. 52 is a combination of two bisphenoids (P and P′), two bipyramids of the second order (b and c), and the basal pinacoid (a). Stannite (Cu2FeSnS4), acid potassium phosphate (H2KPO4), mercuric cyanide, and urea (CO(NH2)2) also crystallize in this class.
Bipyramidal Class
(Parallel-faced hemihedral).
The elements of symmetry are a tetrad axis with a plane perpendicular to it, and a centre of symmetry. The simple forms are the same here as in the holosymmetric class, except the prism {hko}, which has only four faces, and the bipyramid {hkl}, which has eight faces and is distinguished as a “tetragonal pyramid of the third order.”
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| Fig. 52.—Crystal of Chalcopyrite. | Fig. 53.—Crystal of Fergusonite. |
Fig. 53 shows a combination of a tetragonal prism of the first order with a tetragonal bipyramid of the third order and the basal pinacoid, and represents a crystal of fergusonite. Scheelite (q.v.), scapolite (q.v.), and erythrite (C4H10O4) also crystallize in this class.