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the Stefanos pentacycle and the Segre configuration, two closely 
connected figures. 
Referring to Segre’s memoir in Rendiconti di Palermo, Vol. II, 
and to Oosserat’s in Annales de Toulouse Vol. Ill, we may assert 
that the Steeanos 'pentacycle and Segre’s associated sets are essentially 
equivalent figures. In fact, Segre shows that the 5 transversal planes 
to six straight lines form an associated set; herewith is stated that 
the common elements to 6 complexes of-planes in S 4 are the trans¬ 
versal planes to the axes of the degenerated complexes appearing in 
the linear system which is determined by 6 complexes. 
(Hence also follows that these. axes constitute the cubic variety 
with 10 double points, studied by Segre). 
Hence we immediately deduce that the pentacycle may be obtained 
by projecting stereographically the section of a set of associated planes 
urith a hypersphere. 
But now also appears the dual match to the pentacycle: a set of 
associated couples of points , the same being the stereographic projection 
of the section of a set of associated lines with a hypersphere. 
