$$\begin{aligned}x(u,v)&=\frac{2\cos(u)(\cos(u)\cos(2v)+\sqrt{2}\sin(u)\cos(v))}{3\Bigl(\sqrt{2}-\sin(2u)\sin(3v)\Bigr)}\\y(u,v)&=\frac{2\cos(u)(\cos(u)\sin(2v)-\sqrt{2}\sin(u)\sin(v))}{3\Bigl(\sqrt{2}-\sin(2u)\sin(3v)\Bigr)}\\z(u,v)&=-\frac{\sqrt{2}\cos^2(u)}{\sqrt{2}-\sin(2u)\sin(3v)}\end{aligned}$$