Extending each of the simply laced Euclidean diagrams A m, m ≥ 1, D m, m ≥ 4, Ẽ 6, Ẽ 7, Ẽ 8 by one vertex, we construct a family of loop-free corank two diagrams à m2, D̃ m2, Ẽ 62, Ẽ 72, Ẽ 82 (called ...