We prove that every Jordan curve in $$\mathbb {R}^2$$ inscribes uncountably many rhombi. No regularity condition is assumed on the curve.

The sewed focus is one of the singularities planar piecewise smooth dynamical systems. Defined by Filippov in his book 'Differential Equations with Discontinuous Righthand Sides' (Kluwer, 1988), it consists two invisible tangencies either side switching manifold. In case analytic focus-like behaviour, showed that approach to singularity infinite time. For non-analytic we show can be finite cent...