24                   A PRACTICAL TREATISE ON GEMS.
	scribed tube, and twenty-four shorter edges placed over each of its faces. The angles are eight hexagonal and six tetragonal; the latter joined two and two by the three prin­cipal axes. This form varies in general aspect, approach­ing, on the one hand, to the cube ; on the other, to the rhom­bic-dodecahedron.—Ex., fluor spar, gold. 5. The triakisoctahedrons (variety of icosite'trahedron, fig. 5) are bounded by twenty-four isosceles triangles, in eight groups of three, and, like the previous form, vary in general aspect from the octahedron on one side, to the rhombic-dodecahedron on-the other. The edges are twelve longer, corresponding with those of the'inscribed octahe­dron, and twenty-four shorter, three and three over each of the faces. The angles are eight trigonal and six dite-tragonal (formed by eight faces) ; the latter angles joined two and two by the principal axes.—Ex., galena, diamond.
	6. The icositetrahedrons (most common variety, fig. 6) are bounded by twenty-four deltoids or figures with four sides, of which two and two adjacent ones are equal. This form varies from the octahedron to the cube, sometimes approaching the former and sometimes the latter in general aspect. The edges are twenty-four longer and twenty-four shorter. The angles are six tetragonal joined by the