536 
NOTES ON POLYHEDRA. 
[375 
11. Before proceeding further I remark that exclusively of the foregoing axial 
systems of the regular polyhedra the only cases are as follows: 
A. A polyhedron may have a single (/-axis, say A 3 : taking this as the axis of Z 
the table is 
X 
7 
Z 
Rot. Symbol 
90° 
90° 
0° 
7T .7T , 
cos - + sm - . k 
q q 
B. It may have a single q-axis, and (symmetrically arranged in a plane at right 
angles thereto) q 2-axes, say A q , qL 2 . Taking the q-axis as the axis of Z and some 
one of the 2-axes as the axis of X, the table is 
X 
Y 
Z 
Rot. Symbols 
7r 
One (/-axis, | Rot. angle = - . 
90° 
90° 
0° 
7T .7T 7 
cos - + sm - . k 
9 9 
q 2-axes, 
\ Rot. 
angle = 90°. 
0° 
90° 
90° 
i 
7T 
90°-- 
90° 
. 7T . . 7T 
% COS - +7 Sill - 
9 
9 
9 9 
(9- 1)- 
' q 
90° 
9 
90° 
(/1 1) 7T . . (?- 1) 7T 
l cos — -— + ? sin — 
9 9 
and in particular if q = 2, the axes are 3Z 2 and the table is 
X 
7 
Z 
Rot. Symbols 
3 2-axes, \ Rot. angle = 90° 
90° 
90° 
0° 
k 
0° 
90° 
90° 
i 
90° 
0° 
90° 
i