I know already that conic sections (or conics) have been widely explored and many things about them are already known. I was wondering if this sort of exploration has taken place for any other sorts of solids. Spheres, of course, are easy, since each cross section is a circle. I was wondering about things like cylinders, paraboloids, or tori. I am most intrigued by the torus, especially after noticing that, when cut the right way, the cross section forms the shape of a lemniscate.
Does anyone know if the cross sections of any other solids have been investigated already?
"Toric section(s)" should be a more successful search term. I've recently completed an article about toric sections, their equation, short descriptions of their most renowned types and an unexpected relation with the cone-cylinder intersections.
The toric sections: a simple introduction
Hope it helps.