( 204 ) 
are deduced out of the triplets of these five planes as @' out of 
(370), ete. 
In the following pages we will submit the configuration of SRGRE 
to a simple analytical investigation. For this let us consider the 
dualistically opposite figure of fifteen lines and ten three-dimensional 
spaces. 
2. If we begin with the second part of the theorem, then we 
have to deal with the figure consisting of eight lines 
Aj, Ag, Ag, My 
bis bg, da bs 
corresponding in this respect with the wellknown double six of 
Scary, that each of these eight lines intersects only those three 
of the remaining ones, corresponding with them neither in letter 
nor in index. We suppose the four given right lines aj, ag, ag, Ca 
to be given in S, in such a way that among the six connecting 
spaces (4) 4); - + « (43 44) there are not three having a plane in 
common. And 5, is then again the line of intersection of the three 
spaces (a3 44), (aa. da), (as 4%), etc. To this figure which in a previous 
study we considered as the basis of a particular net of quadratic 
curved spaces we therefore gave the name of “double four” (“Ein 
besonderer Bündel von dreidimensionalen Räumen 
zweiter Ordnung im Raum von vier Dimensionen”, 
Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 9, pages 
103—114). 
If we consider the spaces (aj as) and (az a4), it is immediately evident 
that each of these spaces contains four of the eight lines of the 
double four and that this is therefore broken up into the two skew 
quadrilaterals 
(a, ba ag by), 
(bs ag bj ag), 
of which the sides written here under each other meet each other 
in four points of the plane of intersection of the spaces (aj 43) and 
(a, a,). If to begin with we draw only the first of those skew 
quadrilaterals (fig. 1), then it is clear that the lines P, Po and P; F4, 
connecting those points in which the pairs of sides (a, bz) and (a3, b4) 
