. 156. OF COMBINATIONS. 205 



we find m = 2, n = 1 ; and therefore 



(P + n 11 ) = (P 1)2. 



By comparing them in the same way with those for 

 (Pr + n) m (. 95.), or 



1 : 1 : 2 



with m + '. qn . i . ELtl; 



2 m1 



we have m = 3, n = 1, and 



(Pr + n n ) m = (Pr I) 3 . 



In respect to the dimensions of the forms, it is quite in- 

 different which of the two designations we employ, for 

 , they both express exactly the same thing. Yet on account of 

 the number of derivation 3, for the analogy with the pyra- 

 midal system, we rather prefer the latter. The vertical 

 prisms become evident from the consideration of their be- 

 longing to the pyramids. One of them, /, is P 4- 03 on 

 account of its horizontal edges at the intersection with P ; 

 while the other, g, is (Pr + o>) 3 , because the edges of com- 

 bination of this prism with (Pr I) 3 are horizontal. 



The definite designation of this compound form will 

 therefore be, according to the preceding developement, 



Pr 1. P 1. Pr. (Pr I) 3 . P. 

 a led e t 



P + 03. (Pr + C3) 3 . Pr + 03. 

 / S h 



. 156. TESSULAR COMBINATIONS. 



A combination of the tessular system is more 

 particularly said to possess a Tessular Character, 

 if it contains the faces of the original forms pecu- 

 liar to this system (.121 127.), without any 

 halves or fourths (. 128.). 



It would be superfluous to enter here into a minuter 

 detail of the binary combinations, comprised under this 



