25 



the complete set of the six arrows thus obtained has a symmetry 

 which can also be described by the presence of a ternary axis of the 

 first order and a real reflecting plane perpendicular to it. This can 

 easily be seen from a figure or a suitable model. 



If n = 4., we shall find in the same way, that the complete set 

 of different positions reached by the arrow is that represented in 

 the fig. 15. Although ~A appears to be also an axis A of the first 



Fig. 16. 



Fig. 17. 



27T 



order with a period , it is evidently not possible now to 



substitute Z 4 by other symmetry-elements which can completely 

 describe the particular symmetry of the figure thus obtained. 



For n = 5 we shall find on examination, that the axis of the second 

 order A B is also an axis A^ of the first order, combined with a plane 

 of symmetry perpendicular to it. This case is thus evidently wholly 

 analogous to that of the ternary axis of the second order dealt with 

 in the above. 



