Plane Crystallographic Groups: OR Case

Abstract

In this chapter G is a discrete subgroup of E with translation subgroup T ≅ Z² and OP subgroup G⁺ of index 2. Then G = G⁺ ∪ G⁺r, where r is OR and G⁺ is one of the groups G _n , n = 1,2,3,4,6, derived in the previous chapter. Thus G is determined by the values of n, r² and of the conjugates a^r, b^r, s^r. As usual the treatment is case by case, greatly simplified by the following useful dichotomy.