. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 156 PRINCIPLES OF CRYSTALLOGRAPHY,. symbols li Ti l, and the other half by efg. The forms of this system are generally pyramids of twenty-four faces, two orders of twelve-faced pyra- mids, whose faces are perpendicular to the principal section, prisms of twelve faces, two orders of six-faced i^risms, and the base. 7. Tesseral (isometric) system.—Nine planes of symmetry, three of which, A A' A", (Fig. 26,) are similar and at right an- g
. Annual report of the Board of Regents of the Smithsonian Institution. Smithsonian Institution; Smithsonian Institution. Archives; Discoveries in science. 156 PRINCIPLES OF CRYSTALLOGRAPHY,. symbols li Ti l, and the other half by efg. The forms of this system are generally pyramids of twenty-four faces, two orders of twelve-faced pyra- mids, whose faces are perpendicular to the principal section, prisms of twelve faces, two orders of six-faced i^risms, and the base. 7. Tesseral (isometric) system.—Nine planes of symmetry, three of which, A A' A", (Fig. 26,) are similar and at right an- gles to each other; the others tautozonal in pairs, with an A intercalated between each two, B . . B^, at an angle of 45° to them. We select the three which are perpen- dicular to each other for the plane of the axes, and deter- mine the length of the axes by the face 111, which lies in an intermediate zone; we t '"'» thus have— a'= & = c; e = >y = C = 90o The five elements are determined. The most general form, hJcl, consists of forty-eight faces, whose dis- tribution is shown in Fig. 26. In the previous development only the most general form, JiTcl, has been considered; it is, however, very easy by specializing the symbols, as by an equation of two indices, for instance, or by conditions which can be conceived in the projection, to represent all the forms of a system by the number and signs of the faces. We wish, for example, the symbol of the faces of the six-sided, the twelve-faced pyramid of the hexagonal system. Their symbols result from the relation of the zones. On the other hand, a simple inspection of the planes of symmetry of this system shows that a face occurring in the zone [(111) (211) j has on the upper side five similar faces. Thus it results that the symbol of the opposite rhombohedron, similar to the primitive rhombohedron, is (122), according to the formula, (p. 22.) Partial forms have not been included in the above representation, any more
Size: 1674px × 1493px
Photo credit: © Library Book Collection / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthorsmithsonianinstitutio, bookcentury1800, bookdecade1840
