The Pontryagin sphere is a homogeneous, nowhere planar, compact 2-dimensional fractal constructed as an inverse limit of closed orientable surfaces. The Pontryagin sphere arises naturally as the boundary at infinity of the fundamental group of a 3-dimensional hyperbolic pseudo-manifold. We prove that if the conformal dimension of the boundary is less than four, then such a group is action rigid: if it acts geometrically on the same proper metric space as another group, then the groups are virtually isomorphic. A key component of the proof is a generalization of Yang’s Theorem regarding the structure of p-adic actions on a tree of manifolds. This is joint work with Chris Cashen, Pallavi Dani, and Kevin Schreve.