What is "spherinder"

In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3- ball (or solid 2- sphere), radius r and a line segment of radius r:

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

Like the duocylinder, it is also analogous to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment.

It can be seen in 3-dimensional space by stereographic projection as two concentric spheres, in a similar way that a tesseract (cubic prism) can be projected as two concentric cubes.