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, radius r1 and a line segment of length 2r2:
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 can be projected as two concentric cubes.

Relation to other shapes

In 3-space, a cylinder can be considered intermediate between a cube and a sphere. In 4-space there are three intermediate forms between the tesseract and the hypersphere. Altogether, they are the:
These constructions correspond to the five partitions of 4, the number of dimensions.
If the two ends of a spherinder are connected together, or equivalently if a sphere is dragged around a circle perpendicular to its 3-space, it traces out a spheritorus.

Related 4-polytopes

The spherinder is related to the uniform prismatic polychora, which are cartesian product of a regular or semiregular polyhedron and a line segment. There are eighteen convex uniform prisms based on the Platonic and Archimedean solids, plus an infinite family based on antiprisms, and another infinite family of uniform duoprisms, which are products of two regular polygons.