jgo^] Henderson — Graphic Representation. 127 



is given by the equation 



65536 y t z t — 52224^^ — 34816 jy x w x f 27744 w x 9 )# 

 + (65536^^ -f 55296 z t w t — 34816 .*,«/, — 29376 w?)y 

 + (65536 ^j, + 55296^, w, — 52224 ^w, - 44064 w x 2 ) z 

 -j- [55296^ — 52224^^ — 88128 ^ x w x — 34816*^ 



- 58752 y s w I + 55488 ^w, -f 70227 w^ w = [2] 



Now by inspection it is evident that the equations [1] and [2] 

 are identical (aside from the constant factor 3), if 



(*,. 2* «*. «0 = (0, 0, 0, 1). 

 Hence one of the four points 0,, 2 , 3 , 4 lies at the vertex D 

 of the fundamental tetrahedron ABCD. 



I shall next write down the equations of the nine lines #/", 

 ag, ah\ bf, bg, b/i; cf, eg, ch. The first three may be written 

 as follows: 



af\ x = 0, w = 



ag: y = 0, w = 



ah: z = 0, w = 



The line bf may be written 



*/-. (3#+4.y + s = 



J ' t32*-f-27w =0, 



since the equation of plane b takes the form 



17 (32* + 27 w) — 96 (3* + 4jv + z) = 0. 



The line ^ may be written 



, ( 8 ^ + 6^-3^ = 



*' (64^ — 5lw =0, 



since the equation of plane b takes the form 



32 (8# + 6y — 3z) — 9(64y — 51 w) = 0. 

 The line M may be written 



(2^-3^ + 6^0 

 ( 32 * — 17 w =0, 



since the equation of plane b takes the form 



128(2* — 3y -j- 6z) — 27(32*— 17 w) =0. 



