C. XI. 
17 
[739 
739] NOTE ON THE OCTAHEDRON FUNCTION, 
and, substituting these in the remaining equations, they become 
129 
9), 
hedron 
jontain 
.lations 
^ (- 9ce + 8d~) = 0, - 9ce + 8d? = 0, ~ (- 9ce + 8d a ) = 0, 
all satisfied if only — 9ce 4- 8d? = 0. Assuming b = f= 2, the values are 
b, c, d, e, f= 2, 2 V(2), 3, 2 V(2), 2, 
and the form is 
Xy (f + V(2) Xhj + 5w ' y ~ + V(2) XyZ + yi ) ’ 
= xy I X 
2 + V(2) xy + yZ ) ^ xy + 
= x y{ x+ m y ) (* ■ + 7m y ) [x+:y V(2)1 (* + M • 
This is, in fact, a linear transformation of the foregoing form XY(X 4 — F 4 ); for 
writing 
we have 
and therefore 
F ^ + V(2 ) y J’ 
X 2 = x- + (1 + i) V(2) xy + iy 2 , 
F 2 = a; 2 + (1 - i) \/(2) xy - iy 2 ; 
X 2 + F 2 = 2;r{tf + V(2)2/}, 
i*-r>-s.y<2)y(.+JL), 
or finally 
X F (X* - F*) = 4*7(2) xy (x + y) (<r + ^ y) (« + y V(2)} (x + JL.); 
and the two forms are thus identical. 
= 0, 
id last