443 
The faces of the six-faced octahedron are shaded on those of 
the irregular twenty-four-faced trapezohedron in (fig. 2 6, 
Plate III.). & 
The following irregular twenty -four -faced trapezohedrons, 
having faces of crystals parallel to them, have been observed 
in nature. 
i[l f #]; Naumann ; ?r 5 4 3 Miller; b * b* b * 
Brooke, in crystals of pyrite. 
iP-42]; — g 3 ; 7r 4 3 2 ; 6 4 b 3 b 2 , in linneite. 
tP- TT" i T']i ~~~ 2 1 1 > 77 IS 11 7; b 10 b 11 b T , in linneite. 
q a 3 11 
i[l f 3]; — g- 1 ; 7 t321; 5 3 6 2 b l , in cobaltine, hauerite, 
and pyrite. 
5 0# j, i 
3 ; 7r 5 3 1 ; b 5 b 3 b l ,m pyrite. 
10 01 
[12 4]; 
— j 7r 10 6 1 ; b 10 b 6 b l , in pyrite. 
4 2 1; b± b 2 b 1 , in pyrite. 
t[1 S 10]; — 2 ~’ 7T 10 5 1 ; b 10 b 5 b l y in pyrite. 
143. Let y be the supplement of the angle of adjacent faces 
over the edges, such as C^ 2i C 2 $ v C 3 S 5 , &c. 
v that over the edges o x S v o^ 5) o^ 2 , &c. 
Then y is the inclination of normal of face 0 2 o^ 5 to that of 
-fig’* 26, Plate III., but indices of C 2 o->d , are m 1 n. and 
of G 2 o 4 d 8 m 1 n (fig. 31* Plate IV.*). 
Hence cos y = 
— — + i + ~ 
n -| * o 
1 n z 
m* 
i.+4+i 
Also v is the inclination of normal of face C 2 d 6 o j to that of 
C l d ] o 1 (fig. 26 Plate III.), hut indices of C 2 d r o, are m 1 n, and 
of n m 1 (fig. 31*, Plate IV.*). 
— +-+- 
Hence cos ™ 
1 ,+X+i 
m* m 
