Cube (fig. 5). This is bounded by six square faces parallel to the
cubic planes of symmetry; it is known also as the hexahedron. The
angles between the faces are 90 deg., and the indices of the form are
{100}. Salt, fluorspar and galena crystallize in simple cubes.
[Illustration: FIG. 15.--Triakis-octahedron.]
[Illustration: FIG. 16.--Combination of Triakis-octahedron and Cube.]
Octahedron (fig. 3). Bounded by eight equilateral triangular faces
perpendicular to the triad axes of symmetry. The angles between the
faces are 70 deg. 32' and 109 deg. 28', and the indices are {111}.
Spinel, magnetite and gold crystallize in simple octahedra.
Combinations of the cube and octahedron are shown in figs. 6-8.
Rhombic dodecahedron (fig. 13). Bounded by twelve rhomb-shaped faces
parallel to the six dodecahedral planes of symmetry. The angles
between the normals to adjacent faces are 60 deg., and between other
pairs of faces 90 deg.; the indices are {110}. Garnet frequently
crystallizes in this form. Fig. 14 shows the rhombic dodecahedron in
combination with the octahedron.
[Illustration: FIG. 17.--Icositetrahedron.]
[Illustration: FIG. 18.--Combination of Icositetrahedron and Cube.]
In these three simple forms of the cubic system (which are shown in
combination in fig. 11) the angles between the faces and the indices
are fixed and are the same in all crystals; in the four remaining
simple forms they are variable.
[Illustration: FIG. 19.--Combination of Icositetrahedron and
Octahedron.]
[Illustration: FIG. 20.--Combination of Icositetrahedron {211} and
Rhombic Dodecahedron.]
Triakis-octahedron (three-faced octahedron) (fig. 15). This solid is
bounded by twenty-four isosceles triangles, and may be considered as
an octahedron with a low triangular pyramid on each of its faces. As
the inclinations of the faces may vary there is a series of these
forms with the indices {221}, {331}, {332}, &c. or in general {hhk}.
[Illustration: FIG. 21.--Tetrakis-hexahedron.]
[Illustration: FIG. 22.--Tetrakis-hexahedron.]
Icositetrahedron (fig. 17). Bounded by twenty-four trapezoidal faces,
and hence sometimes called a "trapezohedron." The indices are {211},
{311}, {322}, &c., or in general {hkk}. Analcite, leucite and garnet
often crystallize in the simple form {211}. Combinations are shown in
figs. 18-20. The plane A Be in fig. 9 is one face (112) of an
icositetrahedron; the indices of the remaining faces in this octant
being (211) and (121).
[Illustration: FIG. 23.--Combination of Tetrakis-hexahedron and Cube.]
Tetrakis-hexahedron (four-faced cube) (figs. 21 and 22). Like the
triakis-octahedron this solid is also bounded by twenty-four isosceles
triangles, but here grouped in fours over the cubic faces. The two
figures show how, with different inclinations of the faces, the form
may vary, approximating in fig. 21 to the cube and in fig. 22 to the
rhombic dodecahedron. The angles over the edges lettered A are
different from the angles over the edges lettered C. Each face is
parallel to one of the crystallographic axes and intercepts the two
others in different lengths; the indices are therefore {210}, {310},
{320}, &c., in general {hko}. Fluorspar sometimes crystallizes in the
simple form {310}; more usually, however, in combination with the cube
(fig. 23).
Hexakis-octahedron (fig. 24). Here each face of the octahedron is
replaced by six scalene triangles, so that altogether there are
forty-eight faces. This is the greatest number of faces possible for
any simple form in crystals. The faces are all oblique to the planes
and axes of symmetry, and they intercept the three crystallographic
axes in different lengths, hence the indices are all unequal, being in
general {hkl}, or in particular cases {321}, {421}, {432}, &c. Such a
form is known as the "general form" of the class. The interfacial
angles over the three edges of each triangle are all different. These
forms usually exist only in combination with other cubic forms (for
example, fig. 25), but {421} has been observed as a simple form on
fluorspar.
[Illustration: FIG. 24.--Hexakis-octahedron.]
[Illustration: FIG. 25.--Combination of Hexakis-octahedron and Cube.]
Several examples of substances which crystallize in this class have
been mentioned above under the different forms; many others might be
cited--for instance, the metals iron, copper, silver, gold, platinum,
lead, mercury, and the non-metallic elements silicon and phosphorus.