§ 1. XXXIII., XXXIV.] EEY. T. P. KIEKMA^f ON THE THEOEY OE THE POLTEDEA. 153 
The q zoneless polar edges may be tertiaries of zoneless hexarchaxines or triarch- 
axines, or secondaries of zoneless tetrarchaxines or monarchaxines, or poles of zoneless 
triaxines or homozone triaxines, or secondaries in m-zoned homozones, or axes of 2-ple 
monaxine monozones, or of 2-ple monaxine contra] anals. In any case we require no 
account of them symmetry, janal or contra] anal, as these polar edges can never be, like 
polar faces, the sub]ects of constructions. It suffices for our purpose that we know 
exactly the number of all ]anal zoned and zoneless amphigrammic axes. 
Our ob]ect here is to state clearly what our Tables are supposed to contain. The 
mode of obtaining the Tables will be discussed in the sequel. 
Megistration of jgolar and non-jpolar faces ofY-edra Q-acra and Q-acra F-edra. 
Tables C. 
XXXIV. In these Tables will be found all the ]anal poles of the preceding Tables, 
as well as all heteroid polar faces. No symmetry is registered here but that of the face, 
therefore there is no account of poles secondary to the one considered. But the charac- 
ter of the axis (V.) is always suffixed, by one of the abbreviations, 
am.go, am.ed, am.gr, go.gr, go.ed, ed.go. 
We shall write x as the symbol of such abbreviation. 
Zoned polar faces. 
5 F|ZZ'^=a, 
sF]ZZ'[=b, 
^ 2 ragdi s'F\Z7J\=c, 
Z\=d, 
Af+‘’“^sF| Z |■=e, 
Af+‘)’”<’sF^ Z [=f. 
Here s and F are the summits and faces inferior to the A-gon. 
We read that there are c A-gons which have r agonal traces of Z and r diagonal 
traces of Z", of which A-gons some will be ]anal and others heteroid poles. 
Zoned TetrarcMpoles. 
hV/ s-F\Z\=d,, 
^A?L,sF{Z}=^3, 
which, being heteroid poles, could not appear in the preceding Tables of polyarchipoles. 
The y denotes the traces. 
Zoneless polar faces. 
A^sF=g (r>I), 
showing that g A-gons have an r-ple zoneless repetition and the character x of axis, of 
which some will be ]anal and others heteroid poles. 
MDCCCLXII. 
X 
