Self dual Einstein orbifolds with few symmetries as quaternion Kähler quotients

We construct a new family of compact orbifolds O4(Θ) with a positive self dual Einstein metric and a one-dimensional group of isometries. Together with another family, introduced in Boyer et al. (2002) [7] and here denoted by O4(Ω), these examples classify all 4-dimensional orbifolds that are quaternion Kähler quotients by a torus of real Grassmannians.