TuTTON: x-ray analysis and assignment of CRYSTAIvS 97 



one of the 32 classes of possible crystal- symmetry is developed. 

 But with respect to the last sentence of the conclusion — that a 

 crystal can be allocated to two different classes — it is absolutely, 

 fundamentally, wrong and entirely unacceptable. There is 

 no more accurate science than modern crystallography. The 

 old method of regarding crystal-classes as holohedral, hemi- 

 hedral (half the faces suppressed), and tetartohedral (three- 

 fourths of the possible faces suppressed) is gone forever, and 

 crystal classification is now at length scientifically and very 

 definitely based on the possession of fixed elements (planes and 

 axes) of symmetry, every one of the 32 possible classes of crystals 

 having its own absolutely unique elements of symmetry. A 

 structure either possesses the elements of symmetry of a particular 

 class or it does not; there is no halfway house. 



The greatest misconception in the memoir, however, and one 

 which probably gave rise to that just alluded to, is that a space- 

 lattice can be anything but holohedral {e. g., the frequent refer- 

 ence in the memoir to the pyritohedron as a space-lattice). 

 Now there are only fourteen space-lattices, those which Bravais 

 verified and immortalized after their original discovery by 

 Frankenheim, and all are essentially and necessarily holohedral 

 (retaining this term as a convenient one to express full systematic 

 symmetry). They are too simple to be anything else. The 

 three belonging to the cubic system (for all the seven systems 

 are represented among the fourteen) are those having for their 

 elementary cells the cube (No. i), the centered cube (No. 2) 

 which is a cube with a point at the center, and the face-centered 

 cube (No. 3), a cube with a point in the center of each face. 

 If each point of these lattices be imagined to represent a poly- 

 hedron of such a nature that when an unlimited number are 

 packed together in contact, space is completely filled, the No. i 

 polyhedron would be a cube, which is obviously a triparallelo- 

 hedron; that of No. 2 space-lattice would be a cubo-octahedron, 

 an octahedron so far modified by faces of the cube that each 

 octahedral face has the shape of a regular hexagon, the solid 

 being a heptaparallelohedron ; and that of No. 3 would be a 



