§ 1. XXXL, XXXII.] EEV. T. P. KIEOIAN ON THE THEOET OE THE POLTEDEA. 149 
5. Asymmetric Polyedra. 
18. (pa).=0, 
giving the entire number 0 of the solids. 
This completes the Tables A of P-edra Q-acra, in which it is understood that every 
zonal and zonoid signature, and every zoneless repetition (r) will be found entered. 
Another such Table is made of the Q-edra P-acra, which will have the form 
(QP) {Z}=A, 
(QP)Y-{Z}=B, &c., 
where the signatures will differ from the preceding only in the exchange of faces for 
summits, and of zonal for epizonal edges. 
Registration ofjanal poles of R-edra Q-acra and Q-edra Y-acra. 
Tables B. 
XXXII. A janal zoned polar A-gon, which is always the termination ofajanal zoned 
axis, is described by its zonal traces in one of the following manners : — 
\m,di \m,ag K2h,agdi Kn.di \n.ag Kn.mo Kn.mo 
•^ja 5 5 ? “^obj ? "^obj 5 ? "^obj 5 
where m is an odd or even number of traces diagonal or agonal, as the case may be, li is 
any number of diagonal alternate with as many agonal traces, and n is any odd number 
of traces, agonal, diagonal or monogonal, as the case may be, in the pole of a janal or 
objanal axis. 
A janal polar zoneless A-gon is described thus by its repetition, 
A'* 
"^coja^ 
where r may be odd or even, the axis being janal or contrajanal. The summits of the 
A-gon form a sequence of configuration r times repeated in the circuit of the A-gon. 
Def. A janal zoned axis is heterozone, if the polyedron has zones of more than one con- 
figuration. 
Thus all janal zoned axes are conveniently divided into heterozone and homozone. A 
homozone axis or pole has but one zonal signature, as the solid has zones only of one 
configuration (XXII.). A heterozone axis or pole has always two or three zonal signa- 
tures. The 2r-zoned heterozone pole has two different zones about its axis ; the (2r-f-I)- 
zoned heterozone has only one zonal configuration about the principal axis ; but it has 
also a secondary zone of different configuration (VII.). Hence the term heterozone 
applies usefully whether the number of principal zones be odd or even. 
Ileterozone janal polar faces. 
5F{zz'Z"}=«, 
sF{ZZ'Z"}=5, {r^l}, 
A2>-.«?*-sF{ZZ'Z"}=c, 
