228 



if there is one, is destroyed, a different janal symmetry being intro- 

 duced. 



Our signatures give us an exact account of all rhombotomous tes- 

 saraces introduced in coronation, and we can readily enumerate the 

 results of peripolar effacement by mere inspection of those signatures. 



All fundamental and primitive reticulations are given by general 

 formulae, as are also the primary plane reticulations on which they 

 are founded, in terms of their marginal signatures, and of their zonal 

 and zonoid signatures. Every kind of janal symmetry may be seen 

 in these fundamentals and primitives. 



Thus, on the supposition, as before, that we have tables of inferior 

 polyedra, and of the plane and full reticulations, symmetrical or not, 

 we can obtain completely the data B for P-edra Q-acra, and for 

 Q-edra P-acra. 



The data E are what the --zoned homozone polyedra become when 



r=2. They are given by the theory of construction of the homo- 

 zone poles for the general value of r ; and each summit is registered 

 with its zonal and zonoid signature and with its effaceables ; and the 

 results of effacement, ordinary or peripolar, are accurately known. 



The data F are what the r-ple monaxine contrajanals become for 

 r=l. We never descend so low as r=l, except in the construction 

 of penesolids, viz. contrajanal anaxine penesolids. The janal anaxine 

 pairs which crown these and other penesolids are data F. They are 

 registered as perfect edges with their effaceables, and the janal results 

 of effacement are also data F. 



The data A are easily obtained. Every polyarchaxine reduces in 

 one way only to a regular polyedron, on the principal faces of which 

 it is constructed, always by its principal poles. 



The effaced effaceables of a polyarchipolar summit (which exists 

 either on a polyarchaxine or on its reciprocal) are all ordinary, and 

 can be restored in one way only. We conceive them restored about 

 all like archipoles. These poles being removed, a polyedron or a reti- 

 culation is laid bare, which has a marginal signature differing in 

 nothing that needs here be noticed from that of a polar reticulation. 

 By inspection of this signature, we can construct on it a given num- 

 ber of polyarchaxine reticulations of given signatures, and the process 

 differs in nothing from the construction of a polar reticulation, except 



