102 
Mr. Whewell on calculating 
symbol of a dodecahedron, which results from repeating 
each of the six planes (^, q, r). 
§. 2. The Quadrangular Prism. 
17. The quadrangular prism may be right or oblique, and 
its base 'may be a square, a rectangle, a rhombus, or a pa- 
rallelogram. But in all cases we may take one of its angles, 
and make that the origin of co-ordinates ; and taking two of 
our co-ordinates along two edges of the base, and the third 
along the length of the prism, we shall be able to express 
the secondary planes in the same manner as in the case of 
the rhomboid. There will however be some additional con- 
siderations to introduce, since the edges of the prism may be 
of different magnitudes ; and its angles not being symme.- 
trical like those of a rhomboid, we shall no longer have the 
same coexistent planes which we had in the former case. 
In order to introduce the first consideration, let w and y, 
fig. 6, be the co-ordinates in the direction of the edges of the 
base, and 2; in that of the length of the prism. Let the space 
bounded by the co-ordinate planes be filled with small 
similar prisms, and let their edges in the directions x,y, z be 
a, 6, c respectively. Let a secondary plane P Q R be formed, 
by taking away h prisms along the edge oc, k along y, and 
I along sj ; then the lengths of AP, AO, AR will be ha.khjc. 
respectively ; and the equation to the plane will be 
ha^ kb^ Ic 
If we call A ; B ; C ; we shall have the angle be- 
tween any two planes by the formula. Art. 8 ; putting for 
»y P, y and for dy ^,/, their values. But if we make y,— />, 
