Spherinder
Sign in to savethumb|The spherinder can be seen as the volume between two parallel and equal solid 2-spheres (3-balls) in 4-dimensional space, here stereographically projected into 3D. 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:
~5 min read
Encyclopedic overview
8 sectionsContents
- Spherindrical coordinate system
- Measurements
- Hypervolume
- Surface volume
- Proof
- Related 4-polytopes
- See also
- References
thumb|The spherinder can be seen as the volume between two parallel and equal solid 2-spheres (3-balls) in 4-dimensional space, here stereographically projected into 3D. 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: 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 is a rotatope and a toratope.
Excerpted from Wikipedia’s “Spherinder” article, available under the CC BY-SA 4.0 licence.