I was reading about geometrical shapes in $n$-dimensional Euclidean spaces and programming some objects that would share some of their properties in different dimensions, like $n$-spheres. I had somewhere an infinite cylinder class that was represented as "the set of points equidistant from a line" and realized that I could easily extend this definition and thus some of the operations to $n$ dimensions. However, I didn't manage to find a name for a general class representing an "$n$-infinite-cylinder".
In the end, my definition to generalize the object to $n$ dimensions does not correspond to the usual way shapes are extended to $n$ dimensions. While this can correspond to a cylinder in a three-dimensional Euclidean space, it does not correspond to anything I could find a name for in a four-dimensional Euclidean space.
Is there a name for such an object?