( 5(U> ) 



By omission out of (2H,^) of ;i S, remains n (21 1„); by omitting 

 S^ ami /S'j, a (15 j remains the scheme of Avliicii is annlia</iiiatic : 

 each couple of its C/.-Spr^ has four 6'/". points in common. The same 

 number of 15 points forms with 15 other Sp^ (namely Hi as far 

 as J31 included out of the number of thirty-five) a 6/. (15^) of 

 which the scheme is complementary to the anallagmatic (15g). 



Out of the Cf. (35iJ is formed by omission of S^ a Cf. (30iJ; 

 by omission of T a Cf. (25^2) ; <^>^' '^'4 ^^^^^ J' ^ Qf- (20^ J; of two 

 different 7' a Cf. (15,,), identical to the already mentioned one, its 

 points lie in an /S/),,, tlie (35^ J has in each of the twenty -eight 

 other Cf.-R^ such a (153). 



If we add to the Cf. (30, J a system 7' out of (28,,) a Cf. (40, J 

 is formed. 



The Cf. (35, g) is also obtainable out of the diagram of simplexes 

 of the /v ^""^ , the simplex A then falls away entirely, of each of the 

 seven other ones three elements of each kind disappear. The diagram 

 (35ig) consists of seven systems S^ in the chief diagonal, mutually' 

 connected by tillings (SJ, which all degenei-ate into (SJ and (2,). 



By omitting 1, 2, 3, 4 from this ^S'^ we obtain Cff. (30,/;, (25,,), 

 (20, g) and (15^). The (30, J is identical to the already mentioned 

 one, the (15g) however is of another type : not anallagmatic, neither 

 do its points lie in one Spg. 



§ 5. In each of the Sp^ formed by intersection of two Cf.-Sp^ 

 of /i^'i^ lie 12 6y. -points, of which thirtj^-two sextuples are also 

 common to a third Cf.-Spe ; such a sextuple lies thus in an Sj)^, 

 the twelve points form with the thirty-two Sp^ a 6/.(12,g, 32g). 



We can give to the diagram of such a Cf. the following form: 

 (see table p. 507). 



If e. g. we take the Cf-Sp^, formed by the intersection of the 

 Cf-Spe : At and .4 2, the twelve points become respectively: 



^3 = P1 B4:=Q1 



A4.= P2 B3=Q2 



A5 = P3 CQ=QS 



A6 = P4. C5=:Q4: 



A7 = Fd HS=Q5 



A8 = PQ H7=QQ 



The entire Cf consists evidently of two simplexes S^ : P and Q 

 in MöBius-position forming together the part (12g) whilst moreover 

 every triplet of vertices of one simplex with the three non-conjugate 

 ones of the other lie in one Spt, i.o.w. each face of one intersects 

 the non-conjugate one of the other. 



