229 



that we conceive it effected in all the principal faces of the subject. 

 "We can crown, and register all summits with zonal or zonoid and mar- 

 ginal signatures and with effaceables, so that the results of (e = 0) 

 symmetrical effacements about all the principal axes are readily enu- 

 merated. These results are the data A. 



It remains only that we return to the construction of the full and 

 plane reticulations, from which all our marginal charges, if they be 

 not polyedra, are selected. 



The full reticulations are reducible always either to a nucleus line 

 or to a nucleus polyedron, by sections in their external eifaceables. 

 The marginal signature shows always the edges removeable by such 

 sections, and construction proceeds by the rule that no external 

 effaceable of the subject shall be external in the result. All effaceables 

 are here secondary. 



The modifications of symmetry of polar monozone and asymmetric 

 subjects and constructions are expressed in general formula*, and the 

 results are always registered with all signatures without ambiguity or 

 repetition. 



We never construct janal full reticulations except what have, as 

 the word janal implies, a symmetry : and such constructions are 

 always polar, except the objanal monozones and the contrajanal 

 anaxirie full penesoiids. The only difference between these full con- 

 structions and that of mixed reticulations is, that no marginal tri- 

 angles are handled or lost in the process ; and that in the building of 

 an r-ple repetition on a subject of n'-ple repetition, we descend to the 

 value r=l, which gives the asymmetric full reticulations by the for-. 

 mulae for the general value of r. 



The plane reticulations have lastly to be considered. 



All plane r-gonal penesoiids (rQf) having/ 1 1(^ 2) diagonals, 



symmetrical or not, are given by general formulae in terms of their 

 marginal signature, 



[2a2b], (r=4 



that is, in terms of (rfab). The line which crowns this signature is 

 the intersection of a (3 + a)-gon and a (3-f 6)-gon. 



All polar plane reticulations and all monozones which have less 

 than three epizonal edges in the zone, reduce in one way only to a 

 polar or monozone primary, which has no diagonals except the bases 



