( 508 ) 



This connection is I'oi- llie fii-st time possible in Sp.^, the analogon 

 in ;S/>3 wonld be: two tetmhedra in M()iuus- position, where each 

 edge of one intersects the non-conjngate one of the other; of tiiis 

 Cf. (8j, 144), althongh it is possible to design the diagram, the 

 execution is evidently impossible. 



We find for the complete notation of Cf. (12^, 32 J: 



By projecting and intersecting are formed out of these e.g. in 



.S'/j/a Cf. (60„, I6O3) and a Cf. (160,, 240,) of points and right 



lines; in ,^i)^ a Cf. (60.,,, 240J and a Cf. (160,, 32jo) of points 

 and planes. 



^ 6. The points of Sp^ can be conjugated one to one to the 

 linear complexes of the usual three-dimensional space, the Sp^ become 

 linear systems of a^ of these complexes, the Cf. (12ig, 32,) can be 

 represented in our space. 



It is however possible to take the twelve complexes simultaneously 

 special and to regard them as right lines, the thirty-two Sp^ then 

 become linear complexes which each contain a sextuple of the right 

 lines; the Cf. (12i8, 32j) is then realized in right lines and linear 

 complexes of our space. 



We can easily give line-coordinates for such a number of twelve 

 right lines by omitting from the point-coordinates of the twelve points 

 a couple, e. g. X^ and X^, and by letting the six remaining ones 

 satisfy the fundamental relation 



X, X, 4- A', X, -f X, a; = 



So we obtain e. g. the right lines 



