= Solution
For $R>r>0$, the closed curve
$$
\gamma(t)=\bigl((R+r\cos2t)\cos t,\,
(R+r\cos2t)\sin t,\,
r\sin2t\bigr)
$$
is embedded on a torus and satisfies
$$
\gamma(t+\pi)=\operatorname{Rot}_z(\pi)\gamma(t).
$$
After <arc-length parametrization>, it meets all the requirements of part (b). Its bending and twisting vary around the two waves, so neither curvature nor torsion is constant.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-2-symmetric-closed-curve.png]
{title=A symmetric closed curve and its reflections}
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