G4 Mil. H. M. TAYLOR ON A SPECIAL FORM OF THE 
Similarly we see that from a double four 
d 
0 
we can form four double threes i 
a 
e f (J 
and from Figure C we see that from a double three we can form three double fours. 
Hence the number of double fours 
= I X the number of double threes 
= 1.720 = 3 . 180 = 540. 
Similarly from each double live we can form live double fours, and from each double 
four we can form two double lives. 
Hence the number of double lives 
= f X the number of double fours 
= 540 = 2 . 108 = 216. 
Similarly from each double six we can form six double lives, and from each double 
live we can form one double six. 
Hence the number of double sixes 
— ^ X the number of double lives 
= ^.216 = 36 .^ 
^19. Now let us choose one triple tangent plane, say the plane through the lines 
4,6, 5; 
twelve other triple tangent planes pass through one or other of these lines. 
The remaining 45-13 or 32 planes all hold a similar relation to the first plane. 
Let us choose, as a second plane, one of those thirty-two planes, say the plane 
through the lines 
9 ,'8,7. 
With respect to the two triple tangent planes which do not pass through a line in 
^ 5}^ 'X' 
* * 
* Tills result was obtained tirst by SouLAb'Li. 
