( 23 ) 
In the same way the two dual forms of the SegKe configuration 
get their image in our space. 
That this correspondence really leads to a practical construction 
of the pentacycle or its dual figure will be apparent from the extreme 
simplicity of the figures 1 and 2 showing the Segre sets abcde , 
a py de. 
Fig. 2. 
In these figures we have applied the methods of descriptive geo¬ 
metry (see Prof. Schoute’s Lehrbuch cler mehrdimensionalen Geometrie ) 
to obtain the completing fifths e, s to the fours abed, apyd, 
starting from the property, that 
in the double four of planes 
yd 
the points a/o', p/p, y/y', d/d' lie 
in one plane s, this being the com¬ 
pleting fifth to either of the fours 
«07d, «W<f. 
in the double four of lines 
abed 
c! b' c' <T 
the spaces (aa') y (bb'), (cc'), (dd') 
intersect in one line e , this being 
the completing fifth to either of 
the fours ab ed, a’ b' c' of. 
We do not enter into the further constructions, though they are 
simple enough, it being rather our intention to generate these 
remarkable figures by constructions not going beyond our space, and 
basing ourselves ou the more formal side of our correspondence. 
