121 



immediately be seen that the pattern in fig. 106 as a whole possesses 

 'he same symmetry as its net-plane, while that in fig. loj has 

 only a set of parallel quaternary axes perpendicular to tin- plain 



t the drawing. Such a pat- 

 tern therefore appears to 

 at the best the sym- 

 ,etry of its own net-plane, 

 amely if its repeat has 

 xactly the same symme- 

 ry-elements which the net- 

 lane possesses; but if the 

 repeat has a lower sym- 

 metry than the net-plane 

 has, the pattern as a whole 

 iust also exhibit a lower 

 degree of symmetry, pos- 

 sessing only those symmetry- 

 elements which are common 

 to its motif and its net-plane. Fig. 107. 



The same is true in the 



ase in which a tridimensional space-lattice is considered, the points 

 f which are substituted by stereometrical figures of a certain sym- 

 metry, playing the 

 part of repeats for 

 the tridimensional 

 pattern resulting 

 in this way. The 

 pattern as a whole 

 can never have a 

 higher symmetry 

 than its characte- 

 ristic space-lattice 

 has; but often its 

 symmetry is ap- 

 preciably lower, 



because its sym- 

 I-ig. 108. 



metry-elements 



are only those, which its space-lattice and its motif have in common. 

 Closer examination of fig. 108 may soon give the conviction that 

 also in the case where the motif of the pattern has a higher degree 



} /^ \ 



M. 



-^O^ 





