# The Prismic Cylinders

## Construction

The construction we used for
*m*,*n*-duoprisms need not be confined
to finite numbers. Consider what happens if we take the limit of these
duoprisms as *m* approaches infinity.

As *m* increases, the *m*-gonal prisms in the ZW cycle become
closer to being cylindrical. The number of members in the XY cycle start to
increase without bound, but their heights decrease toward zero. At the limit,
the ZW cycle become *n* cylinders, and the XY cycle becomes an
*n*-gonal torus. This produces what we call an *n*-gonal prismic
cylinder.

The above images show the case where *n*=4. The tetragonal prismic
cylinder, or 4-prismic cylinder for short, is the same object as the
cubical cylinder. Here are some other prismic
cylinders:

Mathematically, these prismic cylinders are the Cartesian product of a circular disc and a polygon.

## Properties

Although the *n*-gonal prismic cylinders have *n* 3D cylindrical
surfaces, they can only roll in a single direction. Like the
cubical cylinder, which is the same as the tetragonal
prismic cylinder, all the circles in the cylindrical surfaces lie in parallel
planes, even though the central axes of the cylinders are not parallel to each
other. So all of them can only rotate in the same plane, and the
*n*-cylinders can only roll in a single direction, covering only the space
of a line.