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sign-permanencies. The systems become (that of the signs somewhat 

 differently arranged) : 



By providing each of the rows of letters with each of the sign- 

 combinations there appear sixty-four octuples of algebraic numbers 

 to which we assign the notations II, 12,.... VIII 8. Whether we 

 consider these numbers as homogeneous coordinates of points or as 

 coefficients of equations of Sp, in a Sp„ each element is incident to 

 7 x 4 = 28 of another sort, namely to half of the sign combinations 

 of each letter permutation; so a Cf. (64, 8 ) appears, to be designated 



by K vu . 



As with K 111 it is possible to combine the ^/-elements to sim- 

 plexes A, B, C, D, E, F, G, H in various ways. Such an arrange- 

 ment is i. a.: 



The table indicates that eight vertices of e.g. the simplex A are 

 resp. the points II, 114 etc, according to the former notation, whilst 

 at the same time the eight opposite side-«Sp„ of the simplex are 

 represented by those same notations. 



