11)13] 



on Great Advance in Crystallography 



GSf) 



pnrallelohedm (making 2:5 in all) composed of simple Soliiiokian 

 point-systems compounded of interpenetrating- space-lattices. All the 

 28 paruUelohedra are arranged parallelwise, and fill space without 

 interstices. Tliere are. however, only four types, namely, the cube, 

 the rhombic dodecahedron (which has a second vertically elongated 

 variety^ the cubo-octahedron, and the hexagonal prism, the first 

 three being all of cubic symmetry, and the fourth of obviously hexa- 

 gonal symmetry. They are shown, including the second variety of 

 the dodecahedron, in the next screen picture (Fig. 5). He further 

 considers that all four may he homogeneously deformed into analogous 

 parallelohedra of lower orders of symmetry, without ceasing to fill 

 space when closely packed. Hence, von Fedorow concludes that all 

 crystal structures are of either cubic or hexagonal type, including 

 not only truly cubic and hexagonal crystals, but their deformed 

 derivatives. The cubo-octahedron {e. Fig. 5) is identical with Lord 



b c rl 



Fig. 5. — Fedorow's Types of Parallelohedea. 



Kelvin's " tetrakaidekahedron," the most general parallel-faced cell 

 (a heptaparallelohedron) into which space can be regularly partitioned, 

 and possessing the minimum surface for a given volume. 



Unlike the atomic polyhedra of Pope and Barlow, these parallelohedra 

 of voii Fedorow are either molecular or polymolecular, in the latter 

 e\'ent being made up of a small number of identically or symmetrically 

 similar sub-polyhedra, termed by him " stereohedra," which represent 

 the chemical molecules, just as already explained, when the grosser 

 space-lattice unit is polymolecular, the stereohedra being arranged to 

 Iniild up the main polyhedron (the space-lattice unit) on a definite 

 plan, which may involve mirror-image juxtaposition. For example, 

 a rhombohedral system of stereohedra is shown on the screen (Fig. G), 

 consisting of two kinds, R and L, one sort being the mirror-image of 

 the other. Each rhombohedron representing the combined system 

 is composed of six stereohedra, three of each kind, and a series of 

 points, similarly situated one within each stereohedron R, would 

 constitute a Sohncke point-system, while a " double-system " is 

 obtained by adding a series similarly situated one within each 

 stereohedron L. If a single point were taken to represent analo- 

 gously each rhombohedral set of six stereohedra, we should have a 

 rhombohedral space-lattice produced. 



