Things that are named for their inherent dimensionality regardless of the dimensionality of the space they are contained in are others, such as points (0), line

Things that are named for their inherent dimensionality regardless of the dimensionality of the space they are contained in are others, such as points (0), lines (1), planes (2), general manifolds, vector spaces, etc. Spheres (more properly balls) and cubes (or hypercubes) are understood to have the same number of dimensions as the space they are contained in.