 For any compact simple Lie group "G", there is a unique "G"/"H" obtained as a quotient of "G" by a subgroup

Here, Sp(1) is the compact form of the SL(2)-triple associated with the highest root of "G", and "K" its centralizer in "G".These are classified as follows.The twistor spaces of quaternion-Kähler symmetric spaces are the homogeneous holomorphic contact manifolds, classified by Boothby