( 490 ) 



truncated as far as a third of the edges and (smaller) five-cells for 

 odd nr 



Etc., etc. ^). 



The above results are for the greater part given in the general 

 theorems mentioned above. 



IT. The projection of Mn on a plane through tivo opposite 

 edges cutting the diagonal. 



4. For each value of n the indicated projection — see fig. 1 for 

 n = S and n = 9 — is a rectangle PQQ' P' with the sides 1 and 



dy Q, Qi, Q.,A'Q^^ a, (Ki 



n = 9 



Fig. 1. 



y^n — 1 , which is divided by n — 2 lines PjQi, P^Q^, . ■ • Pn-i Qn-2 

 parallel to the shorter sides PQ, P' Q' into n—1 equal -rectangles.') 



1) We break off here because not until the tliird division do we indicate that 

 everything making its appearance in the section can be regarded as simplex or 

 truncated simplex. 



Tlie symbol which indicates tlie numbers of vertices, edges, faces, etc. for 

 arbitrary n is purposely omitted as its form is rather complicated. 



2) To compare the treatise "On the sections of a block of eightcells, etc." 

 (Yerliandelingen der K. A, v. W., vol IX, N . 7). 



