12-Homogeneity of nth suspensions

A space is said to be 12-homogeneous provided that there are exactly two orbits for the action of the group of homeomorphisms of the space onto itself. Certain conditions on a continuum X are known under which the suspension over X   is 12-homogeneous [17]. In this paper we determine sufficient conditions under which the n  th suspension of a Hausdorff space is 12-homogeneous.