Dowling geometry

A spiric section is a special case of a toric section, in which the intersecting plane is parallel to the rotational symmetry axis of the torus (σπειρα in ancient Greek). They were discovered by the ancient Greek geometer, Perseus in c. 150 BC. Their general mathematical form is quartic

${(r^2-a^2+c^2+x^2+y^2)}^2=4r^2(x^2+c^2)$

where $r$, $a$ and $c$ are parameters.