An n-sphere is an n-dimensional manifold that can be translated, via various means such as diffeomorphisms, to other shapes like an n-dimensional egg. Since it'

An n-sphere is an n-dimensional manifold that can be translated, via various means such as diffeomorphisms, to other shapes like an n-dimensional egg. Since it's the "base" shape, that's what it's called. Note that an n-sphere has no holes.