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

A space is 1 n -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 { Σ n : n ⩾ 3 } such that each continuum Σ n is circle-like, 1 n -homogeneous, indecomposable and each of its proper and nondegenerate subcontinua is decomposable.