143 



Fig. 123. 



Section parallel to (100). 



of the spheres of each of its most closely packed triangularly ar- 

 ranged layers, (fiv. 124). In the centres of the cavities of each triad 

 of spheres, ternary axes of rotation are present perpendicular to 



the different layers just men- 

 tioned, in such a way that they 

 pass simultaneously through a 

 sphere-centre of an adjacent 

 layer b and c; while through 

 the centres of the cavities of 

 every group of six contiguous 

 spheres of two consecutive 

 layers, senary screw-axes pass, 

 of course being also perpen- 

 dicular to the already mentio- 

 ned symmetry-planes. 



The screw-axes do not pass 

 through any sphere-centres at 

 all; but three planes of sym- 

 metry pass through every sena- 

 ry screw-axis and through the centres of the three nearest spheres 

 of consecutive layers. Three double sets of binary axes lie in planes 

 midway betw r een the layers of most closely packed triangularly 

 arranged spheres, and perpendicular 

 to the last described symmetry-planes, 

 and they intersect the senary screw- 

 axes. Through every pair of nearest 

 senary screw-axes a plane of "gliding" 

 symmetry can be brought, which 

 planes are evidently perpendicular to 

 the binary axes just mentioned. In 

 planes midway between the conse- 

 cutive layers, the symmetry-centres of 

 the endless system are situated on 

 every senary screw-axis and at points 

 midway between them. If the value 

 of the translation perpendicular to 

 each layer, by which a sphere of the first layer can be brought to 

 coincidence with a superposed sphere of the third layer, be taken 

 as the parameter of the c-axis, while the distance of two contiguous 

 spheres in each layer is taken as a-axis, --it will be obvious that 



Fig. 124. 



Hexagonal Assemblage of Equal 

 Spheres. 



