SOHNCKE'S POINT SYSTEMS 145 



VII. Cubical system. 



1. Tetartohedry : three equal rectangular double axes 

 of symmetry, and four equal triple axes equally inclined to 

 the double axes. Example : sodium chlorate (NaC10 3 ). 



2. Plagihedric hemihedry: three equal rectangular 

 quadruple axes of symmetry, four triple axes as in the 

 preceding, and six double axes bisecting the angles between 

 the quadruple axes. Example : cuprite (Cu 2 0). 



3. Pentagonal hemihedry: as in No. i, but in addition 

 three planes of symmetry at right angles to the double 

 axes. Example : pyrites (FeSJ. 



4. Tetrahedric hemihedry: planes of symmetry as in 

 No. 3, but in addition six planes which bisect the angles 

 between the former planes. 



5. Holohedry : three equal rectangular quadruple axes 

 of symmetry, four triple and six double axes as before, in 

 addition all the planes of symmetry of classes 3 and 4. 

 Example : galena (PbS). 



4. Sohnckes Point Systems. 



The species of regular gratings in space arrived at by 

 Bravais and Frankenheim, on the assumption of an equal 

 and parallel arrangement throughout the crystal, satisfy 

 the law of rational indices, but do not allow of obtaining 

 all the thirty-two classes of forms described above; they 

 lead indeed to seven systems, but only to fourteen classes l . 



In the year 1879 Sohncke 2 extended this conception by 

 rejecting the restricting condition involved in it, that the 

 arrangement round each molecule in the crystal is not only 

 similar, but parallel. The latter is not necessary with 

 regard to the actual observations on crystals ; or rather it 

 is definitely not always the case. The observation of 

 Baumhauer on calcite, for example, is conclusive on this 

 point. Place a prismatic cleavage block (Fig. 31) firmly 



1 Sohncke, Pogg. Ann. 1867, 132. 75. 



2 Entwickelung einer Theorie der Krystalstruktur, Leipzig. 



K 



