Haptics researchers often endeavor to deliver realistic vibrotactile feedback through broad-bandwidth actuators; however, these actuators typically generate only single-axis vibrations, not 3D vibrations like those that occur in natural tool-mediated interactions. Several three-to-one (321) dimensional reduction algorithms have thus been developed to combine 3D vibrations into 1D vibrations. Surprisingly, the perceptual quality of 321-converted vibrations has never been comprehensively compared to rendering of the original 3D signals. In this study, we develop a multi-dimensional vibration rendering system using a magnetic levitation haptic interface. We verify the system's ability to generate realistic 3D vibrations recorded in both tapping and dragging interactions with four surfaces. We then conduct a study with 15 participants to measure the perceived dissimilarities between five 321 algorithms (SAZ, SUM, VM, DFT, PCA) and the original recordings. The resulting perceptual space is investigated with multiple regression and Procrustes analysis to unveil the relationship between the physical and perceptual properties of 321-converted vibrations. Surprisingly, we found that participants perceptually discriminated the original 3D vibrations from all tested 1D versions. Overall, our results indicate that spectral, temporal, and directional attributes may all contribute to the perceived similarities of vibration signals.