Pseudostationary oblique shock-wave reflections in SF$_6$ were investigated experimentally and numerically. Experiments were conducted in the UTIAS 10 x 18 cm Hypervelocity Shock Tube in the range of incident shock wave Mach number 1.25 < $M_s$ < 8.0 and wedge angle 4$^\circ$ < $\theta_w$ < 47$^\circ$ with initial pressure 4 < $P_0$ < 267 Torr (0.53-35.60 kPa) at temperatures $T_0$ near 300 K. The four major types of shock-wave reflection, i.e. regular reflection (RR), single-Mach (SMR), complex-Mach (CMR) and double-Mach reflections (DMR), were observed. These were studied by using infinite-fringe interferograms from a Mach-Zehnder interferometer with a 23 cm diameter field of view. The isopycnics and the density distributions along the wedge surface are presented for the various types of reflection. The analytical transition boundaries between the four types of shock-wave reflection were established up to $M_s$ = 10.0 for frozen and equilibrium vibrational SF$_6$. An examination of the relaxation length under the present experimental conditions indicated that a vibrational-equilibrium analysis was required. Comparisons of experiment with analysis for transition-boundary maps, reflection angle $\delta$ and the first triple-point trajectory angle $\chi$ verify that the reflections were in vibrational equilibrium. The excellent agreement between the present interferometric results and the numerical results obtained by H. M. Glaz et al. (Proc. int. colloq. on dynamics of explosives and reactive systems [Berkeley] (1985)) with real-gas effects also supports the vibrational equilibrium hypothesis for shocked SF$_6$. The behaviour of the angle between the two triple-point trajectories $(\chi' - \chi)$ is discussed and the unique pattern of DMR with $\chi'$ = 0 was verified experimentally. A numerical analysis for the second triple-point system is obtained for the first time. It is shown that, for a given incident shock Mach number, the highest wedge-surface pressure is achieved through a DMR instead of an RR at high $M_s$.