HOLOSYMMETRIC CLASS (Holohedral; Ditetragonal-bipyramidal.) Crystals of this class are symmetrical with respect to five planes, which are of three kinds; one is perpendicular to the principal axis, and the other four intersect in it ; of the latter, two are perpendicular to the equal crystallographic axes, while the two others bisect the angles between them. There are five axes of symmetry, one tetrad and two pairs of dyad, each perpendicular to a plane of symmetry. Finally, there is a centre of symmetry.
Tetragonal bipyramid of the second or der.—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 { ioi } , { 2oI } , { Io2 }, etc., or { hol } .
Fig. 44 shows the relation between the tetragonal bipyramids of the first and sec ond orders when the indices are { III} and { 'or } respectively : ABB is the face (III ), and ACC is { loll. 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 { 3211, etc., or { hkl}.
Tetragonal prism of the first order.—The four faces intersect the horizontal axes in equal lengths and are parallel to the prin cipal axis ; the indices are therefore { I I o } . This form does not enclose space, and is therefore called an "open form" to distin guish 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 { I Io } with the basal pinacoid { ooi } If the faces { I Io} and { oor } 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 { zoo } .
Ditetragonal prism.—This consists of eight faces all parallel to the principal axis and intercepting the horizontal axes in dif ferent lengths; the indices are { 2I01, { 320 }, etc., or { liko} Basal pinacoid (from irivaE, 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).
Combinations of holohedral tetragonal forms are shown in figs. 47-49; fig. 48 is a combination of a bipyramid of the first or der with one of the second order and the prism of the first order; fig. 49 a combination of a bipyramid of the first order with a ditetragonal bipyramid and the prism of the second order. Compare also figs. 87 and 88.
Examples of substances which crystallize in this class are cassiterite, rutile, anatase, zircon, thorite, idocrase, apophyllite, phosgenite, also boron, tin, mercuric iodide.