Duocylinder

A duocylinder is the Cartesian product of two disks. It is the limit of the n,m-duoprisms as n and m approach infinity, and also the limit of the n-gonal prisminders as n approaches infinity. Its surface consists of two identical tori.

It is a rotatope, thus it is also a toratope, a tapertope, and a bracketope.

Variations of the duocylinder exist where the base circles have different radii. Then the volume is $$\pi^2a^2b^2$$.

Coordinates
Where r is the minor radius of one of the cells:

Points on the face of a duocylinder are all points (x,y,z,w) such that


 * $$x^2+y^2 = z^2+w^2 = r^2.$$

Points on the surcell of a duocylinder are all points (x,y,z,w) such that


 * $$x^2+y^2 < z^2+w^2 = r^2,$$
 * $$z^2+w^2 < x^2+y^2 = r^2.$$

Points in the interior of a duocylinder are all points (x,y,z,w) such that
 * $$x^2+y^2<r^2 \quad\text{and}\quad z^2+w^2<r^2.$$