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hedron or cube (l) is produced, designated by the crystal-lographic sign ; expressing the proportion of the
parameters of its faces, or If a plane is sup-
posed
placed in each edge parallel to one axis, and cutting the two other
axes at equal distances, the resulting figure is the rhombic
dodecahedron (3), designated by the sign 0, the proportion of the parameters of its faces being :
1 : 1. The triakisoctahedron (5) arises when on each edge of the
octahedron planes are placed cutting the axis not belonging to that
edge at a distance from the centre rn which is a rational number greater than 1. The proportion of its parameters is therefore m : 1 : 1, and its sign rnO; the most common varieties being 20, and
30. When, on the other hand, from a similar distance m in
each two semiaxes prolonged, a plane is drawn to the other semiaxis, or
to each angle, an ikositetrahedron (6) is formed ; the parameters of
its faces have consequently the proportion m : 1: m, and its sign is mOm;
the most common varieties being 202 and 303, the former very frequent
in leucite, analcime, and garnet. When, again, planes are drawn from
each angle, or the end of one semiaxis of the octahedron, parallel to a
second axis, and cutting the third at a distance n, greater than 1, then the tetrakishexahedron (4) is formed, the parameter of its faces its sign
and the most common varieties in nature and Finally, if in each semiaxis of the octa-
hedron two distances, m and n, be tak'en, each greater than 1, and m also greater than n, and
planes be drawn from each angle to these points, so that the two planes
lying over each edge cut the second semiaxis belonging to that edge, at
the smaller distance n, and the third axis at the greater distance m, then the hexakisoctahedron (7) is produced, the parameters of which are m : n : 1, its sign mOn, and the most common varieties
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