Tetragonal bipyramid of the second order. This is also bounded by
eight equal isosceles triangles, but differs from the last form in its
position, four of the faces being parallel to each of the horizontal
axes; the indices are therefore {101}, {201}, {102}, &c., or {hol}.
Fig. 44 shows the relation between the tetragonal bipyramids of the
first and second orders when the indices are {111} and {101}
respectively: ABB is the face (111), and ACC is (101). A combination
of these two forms is shown in fig. 45.
Ditetragonal bipyramid (fig. 46). This is the general form; it is
bounded by sixteen scalene triangles, and all the indices are unequal,
being {321}, &c., or {hkl}.
[Illustration: FIG. 46.--Ditetragonal Bipyramid.]
Tetragonal prism of the first order. The four faces intersect the
horizontal axes in equal lengths and are parallel to the principal
axis; the indices are therefore {110}. This form does not enclose
space, and is therefore called an "open form" to distinguish it from a
"closed form" like the tetragonal bipyramids and all the forms of the
cubic system. An open form can exist only in combination with other
forms; thus fig. 47 is a combination of the tetragonal prism {110}
with the basal pinacoid {001}. If the faces (110) and (001) are of
equal size such a figure will be geometrically a cube, since all the
angles are right angles; the variety of apophyllite known as tesselite
crystallizes in this form.
Tetragonal prism of the second order. This has the same number of
faces as the last prism, but differs in position; each face being
parallel to the vertical axis and one of the horizontal axes; the
indices are {100}.
Ditetragonal prism. This consists of eight faces all parallel to the
principal axis and intercepting the horizontal axes in different
lengths; the indices are {210}, {320}, &c., or {hko}.
Basal pinacoid (from [Greek: pinax], a tablet). This consists of a
single pair of parallel faces perpendicular to the principal axis. It
is therefore an open form and can exist only in combination (fig. 47).
[Illustration: FIG. 47. Combination of Tetragonal Prism and Basal
Pinacoid.]
[Illustration: FIG. 48.]
[Illustration: FIG. 49.