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of the lines a, , ag: « « « « as the transformation 
— AF Lg A % + B — Li = Vi 
Tj — to + @3 + %, — A5 = Yo 
Vd — & + &, AI js 
tl + wo + v3 — Ay — #5 = Ya 
which it is possible to write in the reversed form 
Amped IH Ha — Hs 
Ary= Hi Ya HY3 + Ha — Hs 
4%,= 9, +¥2—93 HH jo 
4%= Yi HY HIB — Va Ys 
22, == me) 
these equations pass into 
N= rs Vaan ss 0 
Yo=Y¥s 1 YI 1 Ha 0 
Ys =U5 » HY » I= 0 
VI er NN 
NY 1 Y3 Ya 1 Ys =O 
Moreover the equations of all the fifteen lines of the configuration 
present themselves in the collective formula 
Ip Gan, on EN yi 0, 
where p, 7, 7, 8, t indicate one of the permutations of the five 
indices 1,2,..5. 
The regular representation of the lines obtained in this way 
allows of a very simple geometrical realization. If we suppose for 
simplicity’s sake that the homogeneous system of coordinates y; 
with respect to the five-cell of the spaces y; = 0 is a system of 
