In crystals of this system the angle between any two faces P and Q with the indices (hkl) and (pqr) is given by the equation
| COS PQ = | hp + kq + lr | . |
| √(h² + k² + l²) (p² + q² + r²) |
The angles between faces with the same indices are thus the same in all substances which crystallize in the cubic system: in other systems the angles vary with the substance and are characteristic of it.
Holosymmetric Class
(Holohedral (ὅλος, whole); Hexakis-octahedral).
Crystals of this class possess the full number of elements of symmetry already mentioned above for the octahedron and the cube, viz. three cubic planes of symmetry, six dodecahedral planes, three tetrad axes of symmetry, four triad axes, six dyad axes, and a centre of symmetry.
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| Fig. 13.—Rhombic Dodecahedron. | Fig. 14.—Combination of Rhombic Dodecahedron and Octahedron. |
There are seven kinds of simple forms, viz.:—
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°, and the indices of the form are {100}. Salt, fluorspar and galena crystallize in simple cubes.
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| Fig. 15.—Triakis-octahedron. | Fig. 16.—Combination of Triakis-octahedronand Cube. |