36 CRYSTALLOGRAPHY. 
oid (figs. 25 or 26), and also forms in which only half of the 
sixteen planes of the double eight-sided pyramid, or half the 
eight planes of an eight-sided prism—those alternate in position 
Gg 
—are present (figs. 27, 28). In fig. 27 the absent planes are 
those of half the pairs of planes; and in fig. 28 they inclaae 
one of each of the pairs, as will be seen on comparing these 
figures with fig. 21. 
4, Cleavage,—In this system cleavage may occur parallel to the 
sides of either of the square prisms; parallel to the basal plane; 
parallel to the faces of a square octahedron ; or in two of these 
directions at the same time. Cleavage parallel to the base and 
that parallel to a prism are never equal, so that such prisms 
need not be confounded with distorted cubes. 
5. Irregularities in Crystals—The square prisms are very 
often rectangular instead of square, and so with the octahedrons. 
But, as elsewhere among crystals, the angles remain constant. 
When forms are thus distorted, the four prismatic planes will have 
like lustre and surface markings, and thus show that the faces 
are normally equal and the lateral axes therefore equal. If 
the plane truncating the edge of a prism makes an angle of 
precisely 135° with the faces of the prism, this is proof that 
the prism is square, or that the lateral axes are equal, since the 
angle between a diagonal of a square and one of its sides is 45°, 
and 135° is the supplement of 45°. 
6. Distinctions, —The dimetric prisms have the base different 
in lustre from the sides, and planes on the basal edges different 
in angle from those on the lateral, and thus they differ from 
isometric forms. The lateral edges may be truncated, and the 
new plane will have an angle of 135° with those of the prism, 
in which they differ from trimetric forms, while like isometric. 
The extremities of the prism, if it have any planes besides the 
basal, will have them in fours or eights, each of the four, or 
of the eight, inclined to the base at the same angle. When 
there is any cleavage parallel] to the vertical axis, it is alike 
20. 

