Torus

A torus is the surface of revolution of a circle. That circle's radius is called the minor radius while the distance from the center of the circle to the center of the torus is called the major radius of the torus. If the major radius is greater than the minor radius, it is called a ring torus. If the major radius is equal to the minor radius, it is called a horn torus. If the major radius is greater, it is a spindle torus.

It can also be formed by inflating a circle in one dimension.

It is represented as ((II)I) in toratopic notation.

Its expanded rotatope is the duocylinder.

Coordinates
Where r is the minor radius and R is the major radius:

Points on the surface of a torus are all points (x,y,z) such that


 * $$\left(\sqrt{x^2+y^2}-R\right)^2+z^2=r^2.$$

Points in the interior of a torus are all points (x,y,z) such that


 * $$\left(\sqrt{x^2+y^2}-R\right)^2+z^2<r^2.$$