The Coulomb explosion of tribromomethane (bromoform, CHBr3) induced by 28 fs near-infrared laser pulses is investigated by three-dimensional coincidence ion momentum imaging. We focus on the fragmentation into three, four, and five ionic fragments measured in coincidence and present different ways of visualizing the three-dimensional momentum correlations. We show that the experimentally observed momentum correlations for 4- and 5-fold coincidences are well reproduced by classical Coulomb explosion simulations and contain information about the structure of the parent molecule that could be used to differentiate structural isomers formed, for example, in a pump-probe experiment. Our results thus provide a clear path toward visualizing structural dynamics in polyatomic molecules by strong-field-induced Coulomb explosion imaging.