Octahedron (fig. 3). Bounded by eight equilateral triangular faces perpendicular to the triad axes of symmetry. The angles between the faces are 70° 32′ and 109° 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°, and between other pairs of faces 90°; the indices are {110}. Garnet frequently crystallizes in this form. Fig. 14 shows the rhombic dodecahedron in combination with the octahedron.
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| Fig. 17.—Icositetrahedron. | Fig. 18.—Combination of Icositetrahedronand 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.
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| Fig. 19.—Combination of Icositetrahedron and Octahedron. | 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}.
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| Fig. 21.—Tetrakis-hexahedron. | 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 ABe in fig. 9 is one face (112) of an icositetrahedron; the indices of the remaining faces in this octant being (211) and (121).
| 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).