Triple points occur in steady and unsteady supersonic flows, such as transonic flow over an airfoil or in a jet emanating from a supersonic nozzle. A triple point also occurs when an incident shock is unable to regularly reflect from a wall, a symmetry line (in an axisymmetric flow), or a symmetry plane. At a triple point, really line, three shocks intersect: an incident (I) shock, a reflected (R) shock, and a Mach stem (M). At the intersection, a slipstream (SS), which is a free shear layer in a viscous analysis, is generated. The slipstream is defined by two conditions: the pressure is the same across it, and the velocities on each side are tangent to it. These constraints are the basis for any local triple-point analysis. Triple points are usually discussed within the context of shock wave reflection phenomena (Azevedo and Liu 1993; BenDor 2007; Courant and Friedrichs 1948; Henderson and Menikoff 1998; Hornung 1986; Ivanov et al. 1998; Kalghatgi and Hunt 1975; Mouton and Hornung 2007; Uskov and Chernyshov 2006; Uskov and Mostovykh 2011). The focus here, however, is on triple-point morphology, and not on the reflection process.