This paper describes a concept for superconducting resonators for the acceleration of ions in the velocity range . Such a resonator operates in mode with three loading elements and so can be thought of as a triple quarter wave resonator (3-QWR) providing 4 accelerating gaps. The use of a column to support the three stubs provides a benefit beyond those of the two-stub design (2-QWR). In the 3-QWR, the rf mirror currents in the walls surrounding the stubs need only travel through instead of the in the 2-QWR thus further reducing the current in the demountable joints. As in the 2-QWR, the shape of the column allows control of the frequency splitting between the accelerating and other modes. The copper structure is designed to be coated by a thin superconducting film of niobium or lead for operation at 4.3 K. The particular device reported here operates at 150 MHz with an optimum of 0.04. Its outer cylinder is the same size and shape as for the 2-QWR structure reported previously, in order to minimize construction and cryostat costs. A simple transmission line model is presented and the results of microwave studio and other numerical analyses are discussed. The 3-QWR resonators are appropriate for the upgrade of the low-velocity sections of the ANU Heavy Ion Accelerator Facility and other heavy ion accelerator boosters.