Encyclopaedia Britannica, 11th Edition, "Crocoite" to "Cuba" / Volume 7, Slice 7

by Various

Fig. 34.Pentagonal Dodecahedron.	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.

Fig. 36.—Combination of Pentagonal Dodecahedron and Cube.	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}.

Fig. 38.—Combination of Pentagonal Dodecahedron, Cube and Octahedron.	Fig. 39.—Combination of Pentagonal Dodecahedron e {210}, Dyakis-dodecahedron f {321}, and Octahedron d {111}.

Plagihedral[3] Class

(Plagihedral-hemihedral; Pentagonal icositetrahedral; Gyroidal[4]).

In this class there are the full number of axes of symmetry (three tetrad, four triad and six dyad), but no planes of symmetry and no centre of symmetry.