124 



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

 just the same symmetry as its net-plane, while that in fig. zop has 

 only a set of parallel quaternary axes perpendicular to the plane 

 of the drawing. Such a pat- 

 tern, therefore, appears to 

 have at the best the sym- 

 metry of its own net-plane, 

 namely, if its repeat has 

 exactly the same symme- 

 try-elements which the net- 

 plane possesses; but if the 

 repeat has a lower symme- 

 try than the net-plane has, 

 the pattern as a whole must 

 also exhibit a lower degree 

 of symmetry, possessing 

 only those symmetry-ele- 

 ments which are common to 

 its motif and its net-plane. Fig- 109. 



The same is true in the 



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

 of 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, 

 Fig. no. because its sym- 



metry-elements 



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

 Closer examination .of fig. no may soon give the conviction, that 

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



