440 
ON THE TETRAHEDROID. 
[700 
meeting in points 
0, 
~ß, 
7> 
a" ßy'. a , 
a', 
0, 
-y> 
«"ßy'.ß' 
a", 
ß", 
0, 
«ßy.y", 
, addi', 
a"./3/373", 
7" • «'W. 
0, 
the four points being in fact the vertices of the tetrahedron formed by the four planes 
of the tetrahedroid. Observe that, if the singular planes of the 16-nodal surface in 
their original order are 
1, 2, 3, 4, 
5, 6, 7, 8, 
9, 10, 11, 12, 
13, 14, 15, 16, 
then the planes forming the last-mentioned four systems of planes are 
(1, 8, 11, 14), 
(2, 7, 12, 13), 
(3, 6, 9, 16), 
(4, 5, 10, 15), 
viz. they correspond each of them to a term which in the determinant formed with 
the 16 symbols would have the sign +. 
The equation a!¡3"y = a"fiy is evidently not unique. The triads (a, /3, 7), (a, /3', 7'), 
(a", /3", 7") enter symmetrically into the equation of the 16-nodal surface; by taking 
the singular planes of one of the surfaces in a different order, the equation would 
present itself under one or other of the different forms 
a'/3"y = a!'/3y', a"/3y = a/3'7", a/3'y" = a'/3"y, 
a'/3y" = a"/3'y, a"/3'y = a(3"y', a/3"y' = a{3y". 
Cambridge, 9 December, 1878.