For the form 1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
1 
403 
64 
6 3 
64 
--.6 4 
fi- 2 = 
. 1 
¥ 
5 
4 
5 
¥ 
J?i 
— 5 
— 9 
R 2 — 
. 5 
TT 
4 
¥ 
2 
B, 
— 4 
7 
R 2 — 
, 4 
9 
4 
3 
4 
S x 
— 4 
— T 
R 2 — 
1 
¥ 
1 5 
1 1 
1 5 
~T~ 
Rl 
— 1 5 
~ 2 6 
R 2 = 
1 5 
3 3 
i 
3 
fi 1 
— 3 
5 
R 2 — 
. 1 
¥ 
8. 
5 
8 
Ik 
— 8 
1 3 
R 2 = 
4 
T 
5 
w 
5 
Ri 
5 
— 8' 
R 2 — 
5 
9 
5 
3 
10 
Ik 
— 5 
— 8 
r 2 = 
1A 
1 7 
2 
4 
A 
_ 2 
— 3 
R 2 = 
4 
7 
2 
10 
Bi 
_ 2 
— 3 
r 2 — 
5 
¥ 
1 1 
"5 
1 1 
~¥“ 
Ri 
— 11 
— 16 
r 2 = 
l l 
T9 
16 
4 
Ik 
— 1 6 
~ 2 3 
R 2 — 
1 6 
¥T 
7 
¥ 
7 
fir 
— 7 
— 10 
r 2 = 
7 
1 1 
3 
2 1 
5 
fir 
— 3 
4 
r 2 = 
7 
Tl 
4 
8 
fir 
_ 4 
5 
R 2 — 
8 
Tl 
75. Referring now to (Plate II., fig. 10), we may observe that 
the six-faced octahedron is the form from which all the others 
represented on that plate are derived. 
76. When the indices m and n are equal, and both greater 
than unity, the six-faced octahedron (fig. 10) becomes the 
twenty-four-faced trapezohedron, fig. 11, in which case two 
adjacent faces over the edge Co become in the same plane, 
and the 48 faces of the six-faced octahedron are reduced to 
the 24 faces of the twenty -four-faced trapezohedron. 
77. When the index n becomes infinite, and m is some 
number or fraction greater than unity, the six-faced octahedron 
becomes the four-faced cube (fig. 9), and two adjacent planes 
over the edge Od become in the same plane, and so the 48 
faces of the six-faced octahedron are reduced to the 24 faces of 
the four-faced cube. 
78. When the index m becomes unity, and n is some 
number or fraction greater than unity, the six-faced octahedron 
becomes the three-faced octahedron (fig. 13), and two adjacent 
faces over the edge od become in the same plane, and so the 
48 faces of the six-faced octahedron are reduced to the 24 
faces of the three-faced cube. 
79. When the two indices m and n are both equal to 
unity, the six-faced octahedron becomes theoctahedron (fig. 14), 
and the six faces round each octahedral axis become in the 
same plane, and the 48 faces of the six-faced octahedron are 
reduced to the eight faces of the octahedron. 
80. . When the index m = unity, and n becomes infinite, 
the six-faced octahedron becomes the rhombic dodecahedron 
(fig. 12), and the four faces surrounding the rhombic axes are 
