12-Homogeneous n-fold hyperspace suspensions

We study 12-homogeneity of the n-fold hyperspace suspension of continua. We prove that if X is a decomposable continuum and its n  -fold hyperspace suspension is 12-homogeneous, then X   must be continuum chainable. We also characterize 12-homogeneity of the hyperspace suspension for several classes of continua including: continua containing a free arc, atriodic and decomposable continua, decomposable irreducible continua about a finite set.