Duocylinder

The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r1 and r2: It is similar to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.

A regular duocylinder consists of two congruent cells, one square flat torus face (the ridge), zero edges, and zero vertices.

Intuitively, it may be constructed as follows: Roll a 2-dimensional rectangle into a cylinder, so that its top and bottom edges meet.

It cannot be embedded without distortion in 3-dimensional space, because it requires two degrees of freedom ("directions") in addition to its inherent 2-dimensional surface in order for both pairs of edges to be joined.

The duocylinder is the limiting shape of duoprisms as the number of sides in the constituent polygonal prisms approaches infinity.