( 689 ) 



to point out one or more poljtopes — if not quite regular ones — 

 which with C^ fill the fourdimensional space. We have here in 

 view to give to this question an answer, emanating from the connec- 

 tion of a few results formerly arrived at. 



2. We consider the net {M^,) of the measure-polj topes M^ of 

 space Sp^ and cut this by a space Sp^ normal to a diagonal. This 

 work breaks immediately up into two parts. B'irst the section of 

 space Sp^ with a definite measure-polytope M^ must be found, e. g. 

 with the one, the centre of which has been taken for origin of a 

 rectangular system of coordinates with axes parallel to the edges ; we 

 must next investigate how we can prove from this section in which 

 way the intersecting space Sp^ affects the other measure-poly topes 

 of the net. 



The answer to the first part of this question can be found by means 

 of one of the two diagrams 1 and 2, which we shall therefore discuss 

 successively. Of these diagram 1 is what we arrive at when we project 



zo 



30 

 ZO 



S 



fO 

 30 

 3o 

 fO 

 f O 



^o 

 S 

 5 



/ 



'S 





Fig. 1. 

 Proceedings Royal Acad. Amsterdam. Vol. X. 



47 



