69 



Fig. 79. 

 Zivcone. 



11. The symmetry of the groups D%, 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. 77 the 

 crystalform of the orthosilicate olivine : (Mg,Fe) 2 SiO^ is reproduced 

 as a representative of the group D 1 /, while, as up till now no natural 

 representative of the class D? among crystals is known, an imaginary 

 polyhedron having this symmetry, is drawn in fig. j8. The figures 

 which possess a symmetry D%, have three binary axes perpendicular 

 to each other and three planes of symmetry, each containing two 

 of these binary axes. All so-called orthorhombic (holohedral) crystal- 

 forms, - - which are extremely numerous, - - belong to this class 



In fig. i 12 of Table II (p. 65) a number 

 of instances of these groups among plants and 

 animals are reproduced: so we find here the 

 beautiful silica-structures of Diatomeae: if 

 they be considered similarly developed at 

 their tops and bases, J ) they may be mentioned 

 indeed as very striking examples of the sym- 

 metries: D?, D?, D 1 ! and D f / , and perhaps 

 also of Z)f , in their most elegant shapes. 



As illustrations we have chosen here the following representatives 

 of these two classes : Of the group Z)? : Biddulphia pulchella (fig. i) ; 

 Auliscus elegans (fig. 2)', Navicula dichyma (fig. 3)', of the group 



D% : Triceratium digitate (fig. 4), and 

 Robertsianum (fig. 5)', Actinoptychus con- 

 stellatus (jig. 6). 



Of the groups D% and D? we have chosen 

 as examples the crystalforms of zircone: 

 ZrSiOi (fig. 79; Z)f), and of beryll: 

 Be 3 Al 2 (SiO,) 6 , (fig. 80; ?). 



On Table II, moreover, the following 

 objects have been reproduced of D H 4 : 

 Actinoptychus heliopelta (fig. 7); Amphithe- 

 tras elegans (fig. <?) ; Auliscus crucifer (fig. p) 

 and crattfer (fig. 10). Of the group Cf 



only Aulacodiscus Grevilleanus (fig. n)',a. very fine specimen of this 

 symmetry being also Triceratium pentacrinus, which is, however, 



x ) 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, of course, be 



V 



simply that of the groups : G n . 



Fig. 80. 

 Beryll. 



