Electron Theory of Chemistry to Solids. 723 



to some uniaxial system. If we put electrons at the centres 

 of the faces at right angles to y as well as those at right 

 angles to a?, we get a system with three electrons per cell 

 and again having a uniaxial symmetry. 



Hexagonal Prisms. 



When the electrons are at the corners of a hexagonal 

 prism, since each corner is the meeting place of six prisms, 

 the twelve electrons at the corners of the prism will give an 

 average of two electrons per cell. This would be a suitable 

 arrangement tor a divalent element. The arrangement of 

 electrons would have a symmetry corresponding to that 

 of the hexagonal system in crystallography. If, in addition, 

 we place electrons at the middle points of the flat ends of 

 the prism, each of these points will be shared by two prisms ; 

 this arrangement will give an extra electron per cell, so that 

 there will be on the average three electrons per cell, a 

 possible arrangement for a trivalent element. 



If electrons ;>re placed at the middle points of the six side 

 faces there will be three more electrons per cell, so that each 

 cell will account for five electrons if there are no elec- 

 trons at the flat ends and for six if there are, and would 

 .give arrangements suitable for pentavalent and hexavalent 

 elements. 



The atoms accompanying the electrons will also be 

 arranged in hexagonal prisms ; each of these prisms will 

 have an atom at the centre of each end. 



Fig. 1. 



The RliombiG Dodecahedron. (Fig. 1.) 



There are six corners at which four edges meet and eight 

 at which only three meet ; when the dodecahedra are fitted 

 together so as to fill space each of the four edged corners is 

 the meeting-place of six dodecahedra, and each of the three 

 •edged corners of four ; thus there will, on the average, be 



3 A2 



