24 GEOM ETHICAL DEDUCTION OF SEMIKEGUIAK ETC. 



been numbered from 1 to 48; if p stands for any number, // of 

 the second set is obtained by application of the operation c(=c ) 

 top of the first set. The first set consists of 39 different polytopes; 

 the second set contains only eight new ones. 



Table II gives the 48 nets of expansion (the regular nets included) 

 and of the nets of contraction only the seven new ones, so altogether 

 39 -f- 7 i. e. 46 fourdimensional nets. 



Table III gives the nets of threedimensional space and a table 

 of incidences. 



