§ 1. XXII., XXIII.] EEV. T. P. KIEKMAN ON THE THEOET OF THE POLYEDEA. 141 
Homozones may be easily constructed by drawing janal reticulations like the following: 
The interior marginal triangles are supposed to present in the inferior face of the reti- 
culation precisely the configuration formed by the exterior ones in the upper polar face. 
The first is a 4-zoned homozone reticulation, which becomes a 4-zoned homozone 
polyedron, if crowned in both the upper and lower faces by octaces whose rays pass to 
the eight marginal triangles. 
The second is a 4-zoned monarchaxine reticulation, and becomes a 2-zoned homozone 
polyedron, if crowned in the upper face by an octace upon the four upper marginal 
triangles and upon the four summits 12 3 4, and if crowned below by an octace upon the 
four lower triangles and upon the summits 1' 2' 3' 4'. The same reticulation in the third 
figure becomes a 2-zoned homozone polyedron, if crowned above by a hexace upon the 
four upper triangles and on the points 1 2, and by a hexace below on the lower marginal 
triangles and on the points 1'2', whereby the points 12 1'2' become four zoned triaces. 
XXIII. Mmaxine monozone polyedra. — Let F be a polar face of any 3-j-r-ple zoneless 
axis a of a polyedron P, and let P be placed on a muTor by the face F. The solid (PP') 
formed by P and its image P' is a 3-1-r-ple monozone monaxine polyedron. 
The zoneless axis (««') of the solid (PP') is contrajanal (IV.), and in the plane of the 
mirror there is a 3-fr times repeating zone, where r may be odd or even. 
The zonal signature of the solid is, putting f^=3+r, 
G, 0", 0*}, 
which has gr, zoned summits of g configurations, zoned faces of G configurations, &c. 
Every zoneless feature except the two zoneless poles is read 2r^ times on the r^-ple 
monozme monaxine. 
The designation of monaxine contrajanal belongs to these solids in strictness, as well as 
to those of art. XIX. But there can never be any confusion in our terms, if the zoneless 
polyedra of XIX. be called by that name, which is to be understood as zoneless, if the 
term monozone be wanting. ' 
A 2-ple monaxine monozone is .... 
whose zonal signature 
Z=2{1, 2 , 0'} (a=0). 
The zoneless axis is amphigrammic, 2-ple and contrajanal. Monaxine 
monozones are readily constructed on simple Reticulations like these: 
