A family of circle-like, -homogeneous, indecomposable continua

A space is -homogeneous provided there are exactly n orbits for the action of the group of homeomorphisms of the space onto itself. In this paper we construct a family of continua {Σn:n⩾3} such that each continuum Σn is circle-like, -homogeneous, indecomposable and each of its proper and nondegenerate subcontinua is decomposable.