136 
EEV. T. P. KIEKMAN ON THE THEOEY OE THE POLYEDEA. [§ 1. XX. 
One of these two axes /3y may be an m-ple zoneless principal axis, of which the other 
two axes are secondaries. 
Zoneless triaocines. — When m=2, the three zoneless axes ««', f3, and 7 are all double 
janal axes, and the solid is a zoneless triaxine 'polyedron. 
The zonoid signature of a zoneless triaxine, when it is recorded, has the form 
^=2{(rp+j^+0“}, (<rp4-/y4-a=3), 
showing six poles of three, of two names, or of one only. But we shall see that the 
registration of these signatures in zoneless triaxines is of no use for our purpose. 
Zvery non-polar feature of an x-ple monarchaxine or (r= 2 ) triaxine is read 2 r times 
upon the solid, namely, r times about either extremity of the x-ple janal axis. 
The following are such solids, in the two last of which only half the solid is seen, the 
other half, identical with that seen, being supposed below the paper. 
The soKd A, in which the dotted lines are below the page, is a zoneless triaxine whose 
zonoid signature is (r=2), 
the three axes being amphigonal (pp'), amphiedral, and amphigrammic. 
The solids B and C are 4-ple monarchaxines, half seen, whose zonoid signatures are 
^=4{lpd-0p} for B and for C. 
The former has an amphigonal, the latter an amphiedral principal axis. 
A simple mode of constructing zoned monarchaxines is to draw such reticulations as 
these, where the dark edges are effaceables : 
€ 
The first is a 3-zoned monarchaxine, the second a zoneless triaxine, reticulation, having 
in the page an amphigonal and an amphigrammic axis. If we crown the former in one 
