Wed, 11/11/2009 - 21:36 — david
A crystal zone consists of a series of faces, all of which lie parallel to some one crystal direction and whose intersections with each other are all parallel to this direction. For instance in Fig. 36, p.22, the cube and dodecahedron planes, marked a and d, fall into three zones, each zone being parallel to one of the crystal axes; similarly in Fig. 34 the cube and octahedron faces fall into six similar zones with the edges between the faces lying parallel in each case to one of the diagonal axes of binary symmetry. Fis. 50 and 51, p.26 also show clearly the zonal relations of the isometric form it becomes simple to determine the character of an unknown face. Fig. 52 will help in this respected. It gives in the form of a diagram the positions in relation to each other of all the possible form in the Normal Class. It will be noticed that any face falling in the zone between cube and dodecahedron (or in other words truncating the edge between them) must belong to a tetrahexahedron; similarly any face between cube and octahedron belongs to a trapezohedron; between dodecahedron and octahedron will fall the trisoctahedron; while fall the trisoctahedron; while lastly a face that does not occur in any one of these zones must belong to a hexoctahedron. Therefore, to determine the forms present on any isometric crystal, it is only necessary to discover the crystal; recognize the cube, octahedron, and dodecahedron faces that may be present, or, if they fail, to realize where they would properly occur, and them by applying the principle of zonal relations determine the character of the other forms upon the crystal.