Hydride ligands of transition metal polyhydride complexes with a high coordination number are prone to fluxionality leading to interesting structural dynamics. However, the underlying polytopal rearrangement pathways have been rarely studied. Based on quantum chemical calculations carried out in this work with density functional theory and coupled-cluster theory, two new fluxional mechanisms have been identified for the rhenium polyhydride complex ReH5(PPh3)(2)(pyridine) to jointly account for two consecutive coalescence events in the variable-temperature NMR spectra upon heating: lateral and basal three-arm turnstile rotation. The frequently cited pseudorotation in ReH5(PPh3)(2)(pyridine) (Lee et al. Inorg. Chem. 1996, 35, 695) turns out to be a three-step process including two lateral three-arm turnstile steps and one basal turnstile step in between. The new fluxional mechanisms discovered in this work may also exist in other transition metal polyhydrides.