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Duocylinder

The duocylinder, or double cylinder, is a geometric object embedded in 4- dimensional Euclidean space, defined as the Cartesian product of two disks of radii r and r:


D = {(x, y, z, w)∣x + y ≤ r,  z + w ≤ r}

It is analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment. But unlike the cylinder, both hypersurfaces (of a regular duocylinder) are congruent.