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.
There are seven kinds of simple forms, viz.:—
Tetragonal bipyramid of the first order (figs. 42 and 43). This is bounded by eight equal isosceles triangles. Equal lengths are intercepted on the two horizontal axes, and the indices are {111}, {221}, {112}, &c., or in general {hhl}. The parametral plane with the intercepts a : a : c is a face of the bipyramid {111}.
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| Fig. 44. | Fig. 45. |
| Tetragonal Bipyramids of the first and second orders. | |
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.
| Fig. 46.—Ditetragonal Bipyramid. |
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}.