98 tuti'on: x-ray anai^ysis and assignment of crystal,s 



dodecahedron, a hexaparallelohedron. The point-systems cor- 

 responding to the crystal-classes of lower than the full systematic 

 symmetry are not space-lattices at all, but Sohncke regular 

 point-systems, including in many cases those involving enantio- 

 morphism added by Schonflies, Fedorov, and Barlow, and later 

 also accepted by Sohncke. The pyritohedron, the "hemi- 

 hedral" pentagonal dodecahedron, referred to in the memoir 

 and its accompanying table as a space-lattice, is not a space- 

 lattice, but a Sohncke regular point-system; indeed vSohncke 

 allocates three of his point-systems, Nos. 54, 55, and 56 to the 

 pyrites class 30. As the space-lattice is always holohedral, 

 the suggestion made in the memoir, if carried out, would result 

 in every substance belonging to a class other (lower) than the 

 holohedral class of the system to which it conforms being rele- 

 gated not only to that subsidiary ("hemihedral" or "tetarto- 

 hedral") class in question, but also to the holohedral class of 

 the system, that is, to two different classes of the same system, 

 possessing quite different elements of symmetry, which is absurd. 

 For all structures, even "tetartohedral" ones, have a fundamental 

 space-lattice, about the nodes of which their detailed atomic 

 structure may be considered as grouped. Indeed, the point- 

 systems may quite legitimately be, and often are, considered 

 as composed of interpenetrating space-lattices. 



It cannot, therefore, be made too clear that the space-lattice 

 only determines the crystal system and not the class. It ex- 

 presses the grosser crystal structure, that of the molecules or 

 polymolecular groups, each point or node of the lattice repre- 

 senting a single molecule or the small group of two, three, four, 

 etc., molecules necessary to the complete crystal structure. 

 It is the whole structure, including the detailed arrangement 

 of the atoms in the molecule or group, which determines the class. 

 Pyrites most certainly belongs to the dyakis dodecahedral class 

 30, of which the pentagonal dodecahedron is a prominent form, 

 the third of the five cubic classes; but its space-lattice is No. 3, 

 the centered-face cube, just as in the case of the alkali chlorides. 

 Hauerite is similar, but there is some evidence from the Braggs' 



