The Interstellar Boundary Explorer (IBEX) mission has shown that variations in the ENA flux from the outer heliosphere are associated with the solar cycle and longer-term variations in the solar wind. In particular, there is a good correlation between the dynamic pressure of the outbound solar wind and variations in the later-observed IBEX ENA flux. The time difference between observations of the outbound solar wind and the heliospheric ENAs with which they correlate ranges from approximately two to six years or more, depending on ENA energy and look direction. This time difference can be used as a means of “sounding” the heliosheath, that is, finding the average distance to the ENA source region in a particular direction. We apply this method to build a three-dimensional map of the heliosphere. We use IBEX ENA data collected over a complete solar cycle, from 2009 through 2019, corrected for survival probability to the inner heliosphere. We divide the data into 56 “macro-pixels” covering the entire sky, and as each point in the sky is sampled once every six months, this gives us a time series of 22 points per macro-pixel on which to time-correlate. Consistent with prior studies and heliospheric models, we find that the shortest distance to the heliopause d_HP is slightly south of the nose direction (d_HP ~ 110 – 120 au), with a flaring toward the flanks and poles (d_HP ~ 160 – 180 au). The heliosphere extends at least ~350 au tailward, which is the distance limit of the technique.