970 



triangles, each consisting of four parts. These four parts are found 

 to be triangles respectively of the kind 012, 0J3, 023 and 123. 



Hence a relation as the one described is shown to exist between 

 the four poljtopes e^e^C^^^, e^e^C.^^, e^e^C,^^ and ce.e^e^C^oo- 



The poijtope e^e,e^C\^„ obtained by coiiipositiou of the four primitive 

 forms of course stands alone. 



9. I finally remark that a similar investigation as has been carried 

 out here relative to the C\g^-fa,m[\y , may be undertaken in the same 

 manner with regard to other poly tope-families in fourdimensional 

 and in other spaces. 



In the icosahedron-family for instance a relation as the one described 

 will be found to exist between the polyhedra e^I, ej and ce^e^l. 



In the Cj^-family it exists: 



1. between e^C^^, ce^e^C,^ and ce^e^C^^, 



2. between ^i^jC,^ and e^e^Cj^, 



3. between e,etC\^ and ce^e,efC\^. 



In consequence of the small number of coordinate-symbols the 

 [)roperty is here much less striking than in the case of the C\^^- 

 family. 



