(Parallel-faced hemihedral; Dyakis-dodecahedral).
Crystals of this class possess three cubic planes of symmetry but no
dodecahedral planes. There are only three dyad axes of symmetry, which
coincide with the crystallographic axes; in addition there are three
triad axes and a centre of symmetry.
[Illustration: FIG. 34. Pentagonal Dodecahedron.]
[Illustration: FIG. 35. Dyakis-dodecahedron.]
Here the cube, octahedron, rhombic dodecahedron, triakis-octahedron
and icositetrahedron are geometrically the same as in the first class.
The characters of the faces will, however, be different; thus the cube
faces will be striated parallel to one edge only (fig. 89), and
triangular markings on the octahedron faces will be placed obliquely
to the edges. The remaining simple forms are "hemihedral with parallel
faces," and from the corresponding holohedral forms two hemihedral
forms, a positive and a negative, may be derived.
Pentagonal dodecahedron (fig. 34). This is bounded by twelve
pentagonal faces, but these are not regular pentagons, and the angles
over the three sets of different edges are different. The regular
dodecahedron of geometry, contained by twelve regular pentagons, is
not a possible form in crystals. The indices are {hko}: as a simple
form {210} is of very common occurrence in pyrites.
Dyakis-dodecahedron (fig. 35). This is the hemihedral form of the
hexakis-octahedron and has the indices {hkl}; it is bounded by
twenty-four faces. As a simple form {321} is met with in pyrites.
[Illustration: FIG. 36.--Combination of Pentagonal Dodecahedron and
Cube.]
[Illustration: FIG. 37.--Combination of Pentagonal Dodecahedron and
Octahedron.]
Combinations (figs. 36-39) of these forms with the cube and the
octahedron are common in pyrites. Fig. 37 resembles in general
appearance the regular icosahedron of geometry, but only eight of the
faces are equilateral triangles. Cobaltite, smaltite and other
sulphides and sulpharsenides of the pyrites group of minerals
crystallize in these forms. The alums also belong to this class; from
an aqueous solution they crystallize as simple octahedra, sometimes
with subordinate faces of the cube and rhombic dodecahedron, but from
an acid solution as octahedra combined with the pentagonal
dodecahedron {210}.
[Illustration: FIG. 38.--Combination of Pentagonal Dodecahedron, Cube
and Octahedron.]
[Illustration: FIG. 39.--Combination of Pentagonal Dodecahedron e
{210}, Dyakis-dodecahedron f {321}, and Octahedron d {111}.]