according
to their planes of symmetry, and all stones of the same class, no
matter what their variety or complexity may be, show forms of the same
group. Beginning with the highest, we have—(1) the cubic system, with
nine planes of symmetry ; (2) the hexagonal, with seven planes ; (3)
the tetragonal, with five planes: (4) the rhombic, with three planes ;
(5) the monoclinic, with one plane ; (6) the triclinic, with no plane
of symmetry at all.
In
the first, the cubic—called also the isometric, monometric, or
regular—there are, as we have seen, three axes, all at right angles,
all of them being equal.
The
second, the hexagonal system—called also the rhombohedral—is different
from the others in having four axes, three of them equal and in one
plane and all at 1200 to each other ; the fourth axis is not
always equal to these three. It may be, and often is, longer or
shorter. It passes through the intersecting point of the three others,
and is perpendicular or at right angles to them.
The
third of the six systems enumerated above, the tetragonal—or the
quadratic, square prismatic, dimetric, or pyramidal—system has three
axes like the cubic, but, in this case, though they are all at right
angles, two only of them are equal, the third, consequently, unequal.
The vertical or principal axis is often much longer or shorter in this
group, but the other two are always equal and lie in the horizontal
plane, at right angles to each other, and at right angles to the
vertical axis.
The
fourth system, the rhombic—or orthorhombic, or prismatic, or
trimetric—has, like the tetragonal, three axes; but in this case, none
of them are equal, though the two lateral axes are at right angles to
each other, and
