232 



the asymmetric plane reticulations ROF[2 T w>] are given, whatever he 

 the primaries R'O/*, symmetric or asymmetric, to which they are re- 

 ducible by the above process of effacement. 



And with these we have a complete solution, perfectly easy to cal- 

 culate and register, of the problem of the classification and enumera- 

 tion of the P-edra Q-acra. 



The memoir, which I have the honour to present to the Royal 

 Society, contains all the general formulae of this solution. 



There is nothing to prevent our registering in all marginal signa- 

 tures the exact order of the margins. If this be done, we can crown 

 every reticulation registered by a closed polygon A, made by con- 

 necting margins so that no linear section shall remain. The faces 

 collateral with A would be at the same time constructed, and could 

 be registered ; that is, we could register all the faces collateral with 

 any face in their order. And in crowning by summits marginal sig- 

 natures so registered, we could determine and register the faces of 

 every ^>-ace of the P-edra Q-acra in their order. 



The methods above given are applicable to this more laborious 

 registration of results. If this more tedious process be adopted, the 

 construction of the P-edra Q-acra will be an easy matter. 



I am not aware that anything has been printed on the subject 

 of this theory beyond what I have attempted in the ( Philosophical 

 Transactions,' and in the ' Memoirs of the Literary and Philosophical 

 Society of Manchester,' except a short attempt made some three 

 years ago by M. Poinsot to sketch a beginning of the investigation, 

 which appeared in the * Comptes Rendus.' The attempt was well 

 made, but the results given were not quite accurate. I have it not at 

 hand ; but I know that there is a defective enumeration of the simple 

 solids there considered. 



I have enumerated the polyedra of not more than 18 edges by this 

 method, and I hope shortly to publish the classification and enume- 

 ration of the polyedra of 20 edges and under. 



