Spherinder information

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) of radius r₁ and a line segment of length 2r₂:

${\displaystyle D=\{(x,y,z,w)|x^{2}+y^{2}+z^{2}\leq r_{1}^{2},\ w^{2}\leq r_{2}^{2}\}}$

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, and how a circular cylinder can be projected into 2-dimensional space as two concentric circles.