from Wiktionary, Creative Commons Attribution/Share-Alike License.
- noun mathematics A
four-dimensionalanalogue of a cylinder
from Wiktionary, Creative Commons Attribution/Share-Alike License
A part of the lateral boundary consists of two cylinders joining the ends of the cylinder bases, and the figure may be taken in two ways as a hypercylinder.
In a similar way we may have a hypercylinder with cylinder bases.
Since the cylinders may be generated in a similar manner by a plane curve moving parallel to itself around any one of the parallelograms, we have a parallelogram and a closed plane curve, each playing the part of generating element with the other for directrix in generating one portion of the hypercylinder.
Among the first to be noticed are the hyperprism and hypercylinder with parallel line elements, and the hyerpyramid and hypercone with line elements meeting at a vertex.
The hyperprism with prism bases and the hypercylinder with cylinder bases are, then, particular cases of a class of hypersolids which may be described as follows: Two polygons, or two closed plane curves, or a polygon and a plane curve are placed together so that they intersect but do not lie in a single three-space.