i s h e s the chances of t h e r e be ing su i t ab le pos i t ions of P , A, B o r B' , and A 0 for BA o o r B ' A o = c, p a r t i c u l a r l y for A r r a n g e m e n t s I and IV. Thus, the l ike l ihood is g r e a t e r of having fewer a l t e r n a t i v e o r i en t a t i on s in a c co rd with the t r a c e s QR, RS, and SQ. It is t h e r e f o r e helpful to choose fo r the t r i a n g l e QRS the t h r e e of the four {111} t r a c e d i r e c t i o n s for which c /a is the l e a s t in va lue . In th is way, one would qui te often be involved with only two p o s s i b l e p a i r s of m i r r o r o r i en t a t i ons of {111} p lanes when a t o t a l l y a r b i t r a r y choice m a y have given r i s e to four p o s s i b i l i t i e s . The work is t h e r e f o r e r e d u c e d to some extent .