221 



/. The monozone monaxines with their zonal signatures and their 

 poles ; 



g. The zoneless monaxine contrajanals with their repetition and 

 their poles ; 



h. The m-zoned monaxines with their zonal signatures and poles ; 



t. The monozones, with their zonal signatures ; 



j. The zoneless monaxine heteroids with their axes and repetition ; 



k. The contrajanal anaxine polyedra ; 



I. The asymmetric polyedra ; 



m. The monozone A-gons and A-aces with their traces and zonal 

 signatures ; 



n. The objanal monozone A-gons and A-aces with their zonal and 

 zonoid signatures ; 



o. The janal anaxine A-gons and A-aces ; 



p. The asymmetric A-gons and A-aces. 



And these numbers being registered along with the data preceding 

 for all signatures, we have a complete classification and enumeration 

 of the P-edra Q-acra and Q-edra P-acra, which can be continued to 

 any values of P and Q. 



The difficulty lies in the obtaining of the data A B C D E F G. 

 We begin with (C, D, and G). 



Analysis of a polar or monozone summit of a ~P-edron Q acron V. 



Let p 1 be a polar or monozone ^?-ace, which, if polar, is either a 

 zoned or zoneless termination of an axis. If '--zoned or of r-ple zone- 

 less repetition, there is a sequence of configuration r times read about 

 the pole. 



Any summit m through which lies the triangular section p'mn of 

 the solid is a deltotomous summit about p' ; and if mn be an edge, it 

 is ^ deltotomous edge, about p 1 , or of p'. 



If the deltotomous edge mn be in two faces//', of which /has no 

 deltotomous summits about p' except mn, while /' either has more 

 than two deltotomous summits about p', or is a triangle mnr having 

 r collateral with^', mn is a primary effacealle ofp'. 



If the deltotomous edge mn be in two faces //', of which neither 

 has any deltotomous summits about p' besides mn t nor is a triangle 

 mnr having r collateral with p', mn is a secondary effacealle ofp'. 



VOL. XT. n 



