  We study the 2D isentropic Euler equations with the ideal gas law. We exhibit
a set of smooth initial data that give rise to shock formation at a single
point near the planar symmetry. These solutions are associated with non-zero
vorticity at the shock and have uniform-in-time 1/3-H\"older bound. Moreover,
these point shocks are of self-similar type and share the same profile, which
is a solution to the 2D self-similar Burgers equation. Our proof, following the
3D shock formation result of Buckmaster, Shkoller and Vicol, is based on the
stable 2D self-similar Burgers profile and the modulation method.
