128 



In fig. 115 two non-superposable regular systems are reproduced 

 in projection, which are characterised by a set of parallel trigonal 

 screw-axes perpendicular to the plane of the figures; their points are 

 substituted by perfectly asymmetrical repeats. The repeats of three 

 consecutive layers are distinguished by their colour, and they are 

 tinted more darkly, the nearer they are to the observer's eye. It is 

 obvious that we have here two arrangements, characterised by right 

 and lefthanded screw-axes, and being real non-superposable mirror- 

 images of each other. Crystals whose unsymmetrical molecules were 

 placed in the points of these regular systems, would evidently 

 exhibit true enantiomorphism, as for instance is often observed in the 

 case of crystalline substances endowed with optical rotatory power. 



d. 



f) 



> 



> 



Fig. 115. 



11. With respect to the symmetry of Sohncke's sixty-five 

 regular systems,*we may remark here that they are all characterised 

 by rotations and translations, and that their symmetry is exactly 

 the same as that of the symmetry-groups previously deduced, 

 possessing only symmetry-properties of the first order. If the points 

 in these regular systems be substituted by absolutely arbitrary 

 repeats, the symmetry of the resulting pattern will not be influenced 

 by the specific geometrical nature of these repeats, if the latter only 

 be all identical and placed in an analogous way with respect to 

 the axes of the system. 



But if these patterns should also have symmetry-properties of 

 the second order, e. g. a centrical symmetry or symmetry-planes, 

 then again special symmetry-properties of this kind must be attribu- 

 ted to the motifs themselves, just as appeared to be the case in 

 Bravais' explanation of the lower symmetrical crystal-forms. 





