36 BELL SYSTEM TECHNICAL JOURNAL 



If transformations permitted by symmetry are performed, the d matrix 

 is unchanged. Class 3 has a binary axis only, if we choose this as .V3 and 

 perform the transformation 



a = 0-10 we find: 



d = 



dn —diX 



d = \ —d2\ —dii —d23 d2i dif, —doe 1 



dsz —dzi —dz^ dze/ 



For this to be consistent with the original d matrix the terms with conflicting 

 signs must vanish. 



Applying similar analyses to each of the 32 classes we arrive at the set of 

 matrices: 



Class 1 (asymmetric) /dn dn d^ du d^ diA 



No symmetry d = {d2i (^22 c?23 <^24 c?25 <^26 I (11.01) 



\dzi dz2 dzz dzi dzh dzef 



Class 2 (triclinic pinacoidal), center of symmetry d = (11.02) 



Class 3 (monoclinic sphenoidal 



.V3 is binary d — 



Class 4 (monoclinic domatic) /dn du diz di\ 



Xz plane is plane of '^ ~ \ ^^21 ^22 ^23 J26 1 (11.04) 



symmetry \0 dzi dzb / 



Class 5 (monoclinic prismatic) center of symmetry, d = (11.05) 



Class 6 (Orthorhombic /O du \ (Rochelle) 



bisphenoidal) d = {o ^25 ) (11.06) 

 xi, X2, Xz binary 



Class 7 (Orthorhombic 



Pyramidal) /O dn 0^ 



:V3 binary, .Ti and .V2 d = iO ^24 Ol (11.07) 



planes of symmetry \dz} dz2 dzz 0/ 



