36 



Generally speaking, we can say that all objects possessing a cyclic 

 symmetry C n , have hemimorphic forms. 



In fig. 27 an imaginary fruit-form is represented, which may 

 serve to give some impression of vegetable objects which perhaps 



may possess the symmetry of one of 

 the groups C n . (i. c. of C 6 . l ) 



It is evident that alle these objects 

 must differ from their mirror-images ; if 

 the figures here reproduced, are reflected 

 in a mirror, this fact will be grasped at 

 once 2 ). In many cases only one form of , 

 both ' possible is found in nature; why 

 the other is not produced, can hardly be 

 explained. With the problems relating to 

 this, we shall deal more in detail later on. 

 Fig. 26. 4. II. We shall now proceed to 



Caidum-thiosuiphate (jH2O). ^ e cases w here several axes are si- 

 multaneously present, and begin with the simplest case of this kind, 

 i.e. when two binary axes L 2 and Z/ 2 intersect in the geometrical 

 centre of the figure (fig. 28) at an angle <. In fig. 28 

 the axes L 2 and Z/ 2 are supposed to be in the same plane 

 as the drawing ; ON may be the perpendicular to this 

 plane in 0. Because L 2 is a binary axis (x= 180), a rota- 

 tion round L 2 will simply interchange both ends of the 

 line ON, its lower and upper parts being reversed by 

 it. If now a rotation round Z/ 2 occurs through 180, both 

 ends of ON will interchange once more, ON therefore 

 returning finally to its initial position. Thus ON must be itself 



1) The symbols for these and the following groups are- very convenient in 

 morphology for the purpose of description. They are partly analogous to 

 those of Schoenflies, partly analogous to those of P. Saurel, Zeits. f. 

 Kryst. 50. 1. (1911). 



2) It is a very remarkable fact that in several of the very ancient and 

 universally used religious symbols of many peoples, this axial symmetry is also 



distinctly and preferentially 

 expressed. So in the so-called 

 /y//o/-symbols, mystic emblems 

 of doubtful significance, of 

 which an Arabian, Hindu, and 

 Scandinavian form are reproduced here; and also in a Japanese symbol for 

 "good luck". The symmetry indicated (C 4 and C 3 ) is easily recognisable in 

 these widely spread symbols. 



Fig. 27. 



