Cylinder

A cylinder is a prism based on a disk. It is also the solid of revolution of a rectangle around one of its edges. It has two disks for bases, connected by a lateral surface sometimes referred to as a hose.

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

Coordinates
Where r is the radius of the base and h is the height:

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


 * $$x^2+y^2=r^2 \quad\text{and}\quad z^2=\left(\tfrac{h}{2}\right)^2.$$

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


 * $$x^2+y^2<r^2 \quad\text{and}\quad z^2=\left(\tfrac{h}{2}\right)^2,$$ (disks)
 * $$x^2+y^2=r^2 \quad\text{and}\quad z^2<\left(\tfrac{h}{2}\right)^2.$$ (hose)

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