In this work, the existence and propagation of acoustic Tamm states at the interface of air and a face-centered cubic solid-fluid phononic crystal composed of spherical air voids interconnected by cylindrical air channels are demonstrated. Supercell band structure computations via the finite element method reveal surface bands for Tamm states on (100), (110), and (111) surfaces of the phononic crystal. The states decay sharply into the phononic crystal so that only a two-row slab is sufficient to guide them over the respective surfaces without leakage, as confirmed by finite element simulations. In addition, surface wave propagation along the  direction of the (100) surface is experimentally demonstrated. Ability to confine the Tamm states in all three dimensions is a key aspect in designing few-layer-thick acoustic circuits. Low material filling fraction of the phononic crystal could be leveraged to realize lightweight all-acoustic systems where either bulk or surface states can be incorporated. (C) 2018 Acoustical Society of America.