67 



two successive binary axes. If n be an even number, the figure will have 

 s\niietry-centre; if however n be odd, the group will certainly possess 

 ich n centre too. In every case the principal axis A n will be siniul- 

 nieoiisly an axis Ag n of the second order with a period-number zn . 

 'he M'/n&o/ of these groups shall be D%. 



10. The symmetry of the groups D 1 ^, both for even and 

 for odd values of n, is often 

 met with in nature. 



As instances of this kind 

 in polyhedral forms, in fig. 

 J5 the crystal-form of the 

 orthosilicate olivine : 



(Mg,Fe) 2 SiOi i s repro- 

 duced as a representative of 

 the group D 7 /, while, as up 

 till now no natural represen- 

 tative of the class D 77 among 

 crystals is known, an imagi- 

 lary polyhedron, having this symmetry, is 



Irawn in fig. 76. The figures which possess a symmetry D 7 /, have 

 iree binary axes perpendicular to each other, and three planes of 

 symmetry, each containing two of these binary axes. All so-called 

 ihorhombic (holohedral) crystal- forms, which are extremely numerous, 

 belong to this class. 

 In fig. i 12 of 

 Table II a number 

 of instances of these 

 groups among plants 

 and animals are re- 

 produced : so we find 

 here the beautiful 

 silica-structures of 



Fig. 75- 



Olivine. 



Fig. 77- 



Zircone. 



ni 



Hatomeae: if they be considered similarly p 

 developed at their tops and bases 1 ), they 

 may be mentioned indeed as very striking 

 examples of the symmetries: D*j , D*j , Z) 7 / 

 and Z) 7 /, and perhaps also of Z) 7 /, in their most elegant shapes. 



Fig. 78. 

 Beryll. 



l ) If the upper and basal parts of the silica-boxes are thought to be 

 different, the axis A n will then be heteropolar, and the symmetry will be 

 simply that of the groups: C^. 



