K-cell (mathematics)

Intuition

A ${\displaystyle k}$-cell of dimension ${\displaystyle k\le 3}$ is especially simple. For example, a 1-cell is simply the interval ${\displaystyle [a,b]}$ with ${\displaystyle a<b}$. A 2-cell is the rectangle formed by the Cartesian product of two closed intervals, and a 3-cell is a rectangular solid.

The sides and edges of a ${\displaystyle k}$-cell need not be equal in (Euclidean) length; although the unit cube (which has boundaries of equal Euclidean length) is a 3-cell, the set of all 3-cells with equal-length edges is a strict subset of the set of all 3-cells.