The only type of Mach reflection possible in steady flow is direct-Mach reflection, in which the Mach stem is convex away from the oncoming flow, and the slip plane slopes towards the reflecting surface.
By new results  there is a new configuration of shock waves - configuration with a negative angle of reflection in steady flow. Numerical simulations demonstrate two forms of this configuration - one with a kinked reflected shock wave, and an unstable double Mach configuration, depending on the transition path.
In pseudo-steady flows, the triple point moves away from the reflecting surface and the reflection is a direct-Mach reflection. In unsteady flows, it is also possible that the triple point remains stationary relative to the reflecting surface (stationary-Mach reflection), or moves toward the reflecting surface (inverse-Mach reflection). In inverse Mach reflection, the Mach stem is convex toward the oncoming flow, and the slip plane curves away from the reflecting surface. Each one of these configurations can assume one of the following three possibilities: single-Mach reflection, transitional-Mach reflection and double-Mach reflection.