435 
1911-12.] The Geometry of Twin Crystals. 
viii. Lines with odd co-linear and co-directional cyclic number and point 
(central) symmetry have identical plane and line twinning, and there is no 
point twinning. The twin planes and axes are co-directional. 
1 TJc (in all classes with point symmetry) : 1 UcPL, twin axes of (1) all 
1Uc lllcPL 
twins of plagioclase and other crystals of the I TJc class ; (2) those oblique 
to a plane of symmetry in the II Uc class, as in the case of the Baveno twins 
of orthoclase ; (3) those normal to a pyramid face in the II Be class, as in 
the twins on 112 in redruthite and on 232 in staurolite. 
3 TJc (in III TJc, G Uc) : 3 UcPL, principal axis of phenakite in twin from 
Framont in the Vosges (E. Beyrich, Pogg. Ann., vol. xxxiv., 1835, pp. 
521-2 ; vol. xli., 1837, pp. 328-332 ; La Croix, Mineralogie de la France, 
Paris, vol. i., 1893-5, pp. 204-6). 
1 Be (in II Uc, II Be, IV Uc, IV Be, III Be, VI Uc, VI Be, G Uc, G Be ) : 
1 BcPL, twin axes of (1) the Karlsbad and Manebach twins of orthoclase ; 
