Hexagonal bipyramid (fig. 70), bounded by twelve isosceles triangles each of which are equally inclined to two planes of symmetry. The indices are {210}, {412}, &c., or in general (hkl), where h − 2k + l = 0.

Fig. 69.—Scalenohedron with
inscribed Rhombohedron.
Fig. 70.—Hexagonal
Bipyramid.
Fig. 71.—Hexagonal Prism
and Basal Pinacoid.

Hexagonal prism of the first order (211), consisting of six faces parallel to the principal axis and perpendicular to the planes of symmetry; the angles between (the normals to) the faces are 60°.

Hexagonal prism of the second order (101), consisting of six faces parallel to the principal axis and parallel to the planes of symmetry. The faces of this prism are inclined to 30° to those of the last prism.

Dihexagonal prism, consisting of twelve faces parallel to the principal axis and inclined to the planes of symmetry. There are two sets of angles between the faces. The indices are {321}, {532} ... {hkl}, where h + k + l = 0.

Basal pinacoid {111}, consisting of a pair of parallel faces perpendicular to the principal axis.

Fig. 72.—Stereographic Projection of a Holosymmetric Rhombohedral Crystal.

Fig. 71 shows a combination of a hexagonal prism (m) with the basal pinacoid (c). For figures of other combinations see [Calcite] and [Corundum]. The relation between rhombohedral forms and their indices are best studied with the aid of a stereographic projection (fig. 72); in this figure the thicker lines are the projections of the three planes of symmetry, and on these lie the poles of the rhombohedra (six of which are indicated).

Numerous substances, both natural and artificial, crystallize in this class; for example, calcite, chalybite, calamine, corundum (ruby and sapphire), haematite, chabazite; the elements arsenic, antimony, bismuth, selenium, tellurium and perhaps graphite; also ice, sodium nitrate, thymol, &c.

Ditrigonal Pyramidal Class