There exists a natural higher dimensional generalisation of 4-dimensional ALF gravitational instantons of type A_n: the toric hyperkaehler manifolds of Bielawski and Dancer (2000). There are also known many examples of complete hyperkaehler manifolds, where the asymptotic behaviour of the metric should be described as being QALF of dihedral type. These include various monopole moduli spaces, Hilbert schemes of points on complex ALF surfaces, and, conjecturally, Coulomb branches of N=4 supersymmetric quantum gauge theories. In my talk, I shall present an approach to construction and classification of complete QALF hyperkaehler manifolds of dihedral type. This is a joint work with Lorenzo Foscolo.