219 



1 . Zoned symmetry. A polyedron may have zones of one, of two, 

 or of three configurations. A zone divides the solid, when it is con- 

 structed with the greatest possible symmetry, into halves, of which 

 one is the reflected image of the other. Zoned polyedra are, 



1 . Monozones ; 



2. wz-zoned monaxines ; 



3. Zoned triaxines ; 



4. Zoned monarchaxines, having secondary axes ; 



5. Zoned polyarchaxines, which have the axial systems 



of the regular polyedra. 



The intersection of two zones is a zoned axis. 



The zonal signature gives an account of the number of zonal sum- 

 mit faces and edges, whether polar or non-polar ; but not of the num- 

 ber of edges in the zoned features. 



2. Zoneless symmetry. This is w-ple repetition of configuration, in 

 revolution about a zoneless axis. An axis is janal if two opposite eyes 

 can read at the poles configurations C C', which are either identical, 

 or one the reflected image of the other ; otherwise the axis is hete- 

 roid. A zoned janal axis is objanal when C is C' turned through 

 two right angles. A zoneless janal axis is contrajanal when C is the 

 reflected image of C'. The polyedra of this symmetry are, 



1 . Zoneless heteroid monaxines ; 



2. Zoneless monaxine contrajanals ; 



3. Zoneless triaxines ; 



4. Zoneless monarchaxine janals, having secondary axes; 



5. Zoneless polyarchaxines, having the axial systems of the 



regular polyedra. 



3. Mixed symmetry. In this there is both a zone or zones and 

 one or more zoneless axes. The solids are, 



1 . Monozone monaxines ; 



2. w-zoned homozones, having m zoneless axes. 



A zoned janal axis is homozone when the solid has zones of one 

 configuration only ; otherwise the janal zoned axis is heterozone t i. e. 

 the solid has zones of more than one configuration. 



4. Neuter symmetry. There is neither zone nor zoneless axis, but 

 the edges of the solid fall into pairs ab, a'b' diametrically opposite, of 

 which edges one is the reflected image of the other. 



The polyedra of this symmetry are contrajanal anaxine polyedra. 



