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of its marginal triangles. On this primary as subject the reticula- 

 tions in question are constructed by one operation, by charging its 

 marginal triangles with marginal triangles of inferior reticulations, 

 whereby two marginal triangles disappear for every charge imposed. 

 The number and the symmetry of the constructions are always given 

 by inspection of our signatures. The monozones which have more 

 than two epizonal edges in the zone, reduce by section in the central 

 epizonal or epizonals to two or to three inferior zoned reticulations. 



We construct, conversely, a given marginal and zonal signature thus 

 in every possible way, the number of constructions being always given 

 by inspection of our tables. All polar reticulations having this zone 

 and marginal signature will be formed by the process. The polar 

 being already registered^ the monozones are obtained by subtraction. 

 Perhaps the greatest difficulty in the theory of the polyedra is 

 the enumeration of the M asymmetric plane reticulations which have 

 the marginal signature 



S=[2 T u>], 



where 2 T means simply 2T ; and where T is the number of the mar- 

 ginal triangles, and w that of the submarginal edges, of which no 

 two are contiguous. The reticulations to be found will be registered 



ROF[2Vj=M, 

 where 



Y-l-T=d 



is the number of diagonals which are not bases of marginal triangles, 

 and 



is the number of the summits of the reticulation, of which s only are 

 not summits in marginal triangles. If we erase the d diagonals, and 

 also the s diaces that they may leave (summits of two edges), we 

 have a primary reticulation, 



B/0/[2 T ], (R'=2T + w), 



which mayor may not be polar or monozone. If now on the u sub- 

 margins of R/0/ we deposit s points (diaces) in every possible way, 

 and then draw in the 



enclosed by the T marginal triangles d diagonals in every possible 



