Noncircular algebraic curves of constant width: an answer to Rabinowitz

Abstract In response to an open problem raised by S. Rabinowitz, we prove that $$ \begin{align*} \begin{array} [c]{l} \left( x^{2}+y^{2}\right) {}^{2}+8y\left( y^{2}-3x^{2}\right) \right) {}^{2}+432y\left( 351-10\left( \\ =567^{3}+28\left( {}^{3}+486\left( 67\left( -567\times18\right) \end{array} \end{align*} is the equation of a plane convex curve constant width.