The standard n-ball is $B^n = \{x \in \mathbb{R}^n | \quad ||x|| \le 1 \}$ where $||x||^2 = \sum_{i=1}^n {x_i}^2 $ The standard n-ball is also called the unit n-ball or the n-disk.

The notation in the literature for the standard n-ball is not uniform. Sometimes it is denoted by $V^n$ , $D^n$ ,$E^n$ or ${\overline{E}}^n$

The boundary of the standard n-ball is $S^{n-1}$ the n-1-sphere.

A space that is homeomorphic to the standard n-ball is called an n-cell.

A 1-cell is called an arc and a 2-cell is called a disk.