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It is shown that the $\gamma$-van der Waals equation of state (eos) permitsshock polars with supersonic critical points, corresponding to critical orstrong-type shock reflections that are supersonic, which is not possible forideal gas. It is also shown that general van der Waals eos permit polars withmultiple critical points, corresponding to four or more reflected shocks forsame deflection angle. Of these reflected shocks at least two are weak-type,i.e.\ deflection angle increasing with increasing shock strength, so thatstandard literature has no criteria to select one of the two. Both phenomenacan be found with Hugoniot curves entirely in the region of convex andthermodynamically stable eos, avoiding the coexistence region and satisfyingvarious shock stability criteria.

Van der Waals shock polars with multiple or supersonic critical points