162 Transactions of the Royal Society of South Africa. 
the rhombs of the dodecahedron. The grain, therefore, is equally inclined 
along six planary directions of the three rectangular axes. 
Taking any complete set of six planary directions : 
(1) They meet a face of the octahedron in two sets of three each, of 
which one set is at right angles to the face, the otlier inclined 54° 
44' to the normal. The grain of the first set is inclined 35° 16' to 
the normal ; that of the second runs parallel to the surface. 
(2) They meet a face of the rhombic dodecahedron, one of them at 
right angles, the grain being also parallel to the shorter diagonal 
of the rhomb, one flush, as also the grain, with the longer 
diagonal, and four inclined at 30° to the normal, while the 
I'espective grainings of these are inclined at 54° 44' to the edges. 
(3) They meet a face of the cube, two being at right angles to this, 
themselves intersecting at right angles, the grain of each being 
parallel to a diagonal of the face, and four at equal inclinations of 
45°, as also their grainings. 
Hence, having regard to these planary directions, if a diamond crystal- 
lises in dependent grained parallel laminae, then the octahedron, the rhombic 
dodecahedron and the cube, are the regular forms most likely to occur. 
Transition forms such as the triakis- and hexakis-octahedron, if there be 
such things, would be due to accelerated growth in the central parts of the 
planary directions cutting the faces of the octahedron ; but there is no 
obvious reason why diamonds alleged to be of such forms shoulddiave the 
exquisite symmetry assigned to them in treatises on crystallography. 
The geometrical patterns displayed on the faces of diamonds appear to 
be due to the grainings which run parallel to a face. Thus are derived the 
shallow triangular indentations on the faces of the octahedron — shallow,, 
because their sides are normally parallel to similarly oriented dodecahedron 
faces, and the square indentations on the faces of the cube, these squares 
being apparently mostly confused by the intrusion of the grainings which 
meet the faces aslant. Again, the parallel striations appear whenever the 
grain of a planary direction runs flush with a face, as in the rhomb of the 
dodecahedron, and across a bevelled edge of the cube. 
Rounded forms are entirely a dodecahedral efl'ect. To be quite precise,. 
there is no such thing as a rounded octahedron, though the term may pass 
for the sake of convenience. An octahedron can only be thicker through 
the middle of opposite faces than at the edges when its edges are terraced by 
the imposition, step upon step, of smaller and smaller triangular slices — the 
form which for some reason has been classed as a tetrahedral twin.* The 
* The tetrahedral theory introduces much mental complexity into the study 
of the crystallisation of diamond. And although it may be invoked with some 
appearance of justification to explain a single-grooved edge to a diamond (cf. Lewis, 
p. 481), or a made such as Fig. 1, it is less satisfactory when there are many groovea 
(and these with striated, not smooth edges), as is usually the case. 
