Two misshapen or distorted octahedra are represented in figs. 85 and 86;
the former is elongated in the direction of one of the edges of the
octahedron, and the latter is flattened parallel to one pair of faces.
It will be noticed in these figures that the edges in which the faces
intersect have the same directions as before, though here there are
additional edges not present in fig. 3. The angles (70 deg. 32' or 109
deg. 28') between the faces also remain the same; and the faces have the
same inclinations to the axes and planes of symmetry as in the equably
developed form. Although from a geometrical point of view these figures
are no longer symmetrical with respect to the axes and planes of
symmetry, yet crystallographically they are just as symmetrical as the
ideally developed form, and, however much their irregularity of
development, they still are regular (cubic) octahedra of
crystallography. A remarkable case of irregular development is presented
by the mineral cuprite, which is often found as well-developed
octahedra; but in the variety known as chalcotrichite it occurs as a
matted aggregate of delicate hairs, each of which is an individual
crystal enormously elongated in the direction of an edge or diagonal of
the cube.
The symmetry of actual crystals is sometimes so obscured by
irregularities of growth that it can only be determined by measurement
of the angles. An extreme case, where several of the planes have not
been developed at all, is illustrated in fig. 87, which shows the actual
shape of a crystal of zircon from Ceylon; the ideally developed form
(fig. 88) is placed at the side for comparison, and the parallelism of
the edges between corresponding faces will be noticed. This crystal is a
combination of five simple forms, viz. two tetragonal prisms (a and m,)
two tetragonal bipyramids (e and p), and one ditetragonal bipyramid (x,
with 16 faces).
[Illustration: FIG. 87.--Actual Crystal.]
[Illustration: FIG. 88.--Ideal Development.