222 



The summit p' has e (^f 0) effaced effaceables. These can be re- 

 stored in one way only, since each (mn) must complete a face /which 

 has no deltotomous summit besides mn. Let them be restored. 

 We have the perfect summit p' (i. e. a summit which has no effaced 

 effaceables) of a (P + <?)-edron Q-acron V /5 which has E = e effaceables. 



The process whereby the data C, D are obtained is the construction 

 in groups of all perfect polar p-aces and monozone p-&ces having a 

 diagonal zonal trace, of all the (P + e)-edra Q-acra (V ; ), which can 

 be reduced by effacement of e effaceables to a polar or monozone ^-ace 

 of a P-edron Q-acron V. These polyedra V y can be all constructed 

 about their perfect poles and registered ; for no result of effacement 

 is small enough to be employed in the construction of a polyedron 

 (V,). Each perfect ^>-ace p f constructed has E(^e) effaceables, which 

 are registered with the signatures of symmetry ; so that all results 

 of effacing e(=Q) of the E effaceables about any registered perfect 

 |j-ace are exactly known without repetition, and without enumeration 

 of two summits, of which one is the reflected image of the other. 



The process of this construction of perfect p-aces p' is the converse 

 of the reduction ofp f . 



In the reduction of p', we remove all the rays of p', whereby we 

 lay bare either a polyedron or a reticulation, which has among its 

 linear sections the E effaceables ofp'. 



If the effaceables of the reticulation are all secondary, it is a full 

 reticulation, which is an agglutination of polyedra cohering by those 

 secondary effaceables, which are linear sections, and the only linear 

 sections, of the reticulation. 



If the reticulation has no effaceables, it is aplane reticulation, being 

 simply a polygon partitioned by certain diagonals. 



If there be one or more primary effaceables, we have a mixed reti- 

 culation. 



The mixed reticulation always reduces in one way only by sections 

 in its external primary effaceables, to a subject reticulation, which is 

 either mixed or full or plane, or else to a polyedron. And, by conti- 

 nuing this reduction, we always obtain finally a full reticulation, a 



plane reticulation, or a polyedron, -zoned, or of n'-ple zoneless 



repetition. 



The primary effaceables of a mixed reticulation are the joints or 



