In [R. Craigen, C. Koukouvinos, A theory of ternary complementary pairs, J. Combin. Theory Ser. A 96 (2001) 358–375], we proposed a systematic approach to the theory of ternary complementary pairs (TCPs) and showed how all pairs known then could be constructed using a single elementary product, the natural equivalence relations, and a handful of pairs which we called primitive. We also introduc...