128 Mr. Whewell on calculating 
The regular triangular prism ; - {pi 
(p,p — q; — r) 
(q, q —p; — r) 
The rhombic dodecahedron ; - - pi 
iP, < 7 . —p + q + r) 
[P> —p + q+r,r) ' 
{—p + q + r, q, r) 
A crystal may be represented by uniting the symbols of 
the planes of which it is composed. And it will be conve- 
nient to represent by a figure in brackets thus (6), the num- 
ber of faces which arise from each symbol. Also frequently 
the crystal has parallel planes; in which case one of them may 
be considered as a repetition of the other ; and the plane thus 
doubled may be indicated by writing a 2 before it. Thus 
the form of borate of magnesia, called by Hauy magnesie 
horated defective, may be thus represented. 
Primary ; a cube. 
Secondary; 2 (3) (i , o, o) + 2 (6) (± i , 1 , o) + (4) (± 1 , 1 , 1) 
Indicating — a cube 2(3) (1,0,0), formed by repeating 
each of the primary planes (1, o, o) ; 
Modified by 6 pairs of planes (±1,1,0); truncating the 
edges ; 
And by 4 planes truncating angles, which are not repeated. 
Hence the opposite angles are not symmetrically affected. 
The situation of planes with respect to each other, may be 
determined by assuming a certain point as the pole of the 
crystal, and measuring the latitude and longitude of the cen- 
tre of the plane with respect to this pole. If we suppose an 
ellipsoid of which the three axes are as the three edges a, 6, c 
of the primitive form, we may suppose secondary planes to 
