439 
hedron, and fonr-faced cube, which have no hemihedral forms 
with inclined faces, are limiting forms of the six-faced tetra- 
hedron. 
Also that all the formulae of the tetrahedron, three-faced 
tetrahedron, and twelve-faced trapezohedron may be derived 
from those of the six-faced octahedron by giving the proper 
values to m and n . 
139. Table showing the symbols and formulae of the half- 
symmetrical forms which are not included in the table § 131, 
for the holohedral forms. The letters refer to holohedral forms, 
§ 131. 
SIX-FACED OCTAHEDRON. 
Naumann. 
Miller. 
Brooke. 
Ratio ^ ^ 
Angle w. 
AO 
SA(H3) 
3 0 4 . 
~~2 
k 3 2 1 
-H^fc 4 ) 
3 
f 
69° 5' 
il(45) 
5 04 
* $***&*) 
2 
jc 5 3 1 
5 
r 
57 7 
THREE-FACED 
TETRAHEDRON. 
1 (1 4 f) 
0-* 
2 “ 
k 2 2 3 
i(a 4 ) 
1 
1 
j 86° 38' 
A (12 2) 
202 
2 
K 1 1 2 
1 
70 32 
l 4 (1 3 3) 
303 
2 
K 1 1 3 
±(a 3 ) 
1 
50 29 
4(144) 
404 
2 
K 1 1 4 
jr(a 4 ) 
1 
38 57 
m}(l 5 5) 
505 
2 
K 1 1 5 
\ (a 5 ) 
i 
31 35 
TWELVE-FACED 
TRAPEZOHEDRON. 
U(i i i) 
4 0 
2 
/C 2 3 3 
3 
•¥ 
97° 51' 
h i (1 1 2) 
2 0 
i 
2 
* 1 1 2 
¥ ( a 4 
2 
"3* 
90 0 
TETRAHEDRON. 
O i (1 1 X) 
O 
2 
Kill 
*(o?) 
1 
109° 28' 
140. The pentagonal dodecahedron is a half- symmetrical 
form with parallel faces derived from the four-faced cube. It 
