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seams by which it can be either taken to pieces or constructed, in one 

 way only. And the portions into which it breaks up by these joints, 

 are either polyedra, or full reticulations, or plane reticulations, of 

 which we have an account in our register. 



We first suppose given all plane and full reticulations, as well as 

 the inferior polyedra, with all their signatures. By means of these, 

 imposed as marginal charges on a subject reticulation, we can con- 

 struct and register exactly all polar and monozone mixed reticula- 

 tions, with their repetition and zonal signatures, and with their 

 effaceables, which are always edges that have been loaded with mar- 

 ginal charges. 



Every reticulation, plane, full, or mixed, is registered with its 

 marginal signature. 



The marginal signature exhibits to the eye all that is requisite to 

 be known either for the coronation of the reticulation by a p-SLce p' t 

 whereby it becomes a polyedron, or for the construction on it of higher 

 reticulations. The marginal signature to be constructed can always 

 be exactly written ; and there is a given number of ways of constructing 

 it on the subject signature, which can be registered, and the number 

 is obtained by inspection of our signatures. We always see in a mixed 

 marginal signature what is removeable by sections in the external pri- 

 mary effaceables, and in a full reticulation we see what is removeable 

 by external secondary effaceables. 



The rules for charging a subject marginal signature, so as to con- 

 struct another signature upon it, are : 



1 . No primary effaceable which is external in the subject is to be 

 external in the constructed; therefore the subject compartment 

 standing on every external primary effaceable must receive at least one 

 charge, which charge will be a compartment of the new signature. 



2. Solid charges (polyedra or full reticulations) are imposed on 

 plane marginal triangles of the subject. Plane reticulations, which 

 give plane compartments, are imposed on solid marginal edges of the 

 subject by a marginal triangle of the charge, which is lost in the 

 operation, or supposed to be cut away. Thus a marginal triangle is 

 lost by every charge imposed, whether plane or solid. 



We handle all plane reticulations only by their marginal triangles, 

 given by their signatures, and thus we escape the necessity of keep- 

 ing any account of their summits. 



