A point has 0 dimensions.

 

A line has 1 dimension, length, bounded by 2 (0 dimension) points.

 

A square has 2 dimensions, height and width, bounded by 4, 1 dimensional lines. (8 0 dimension points)

 

A cube has 3 dimensions, height, width and depth, bounded by 6, 2-dimensional squares, made up of 24 1 dimensional lines. (48 0 dimension points)

 

A 4-dimensional "space" is made up of 8, 3-dimensional cubes, made up of 48, 2-dimensional squares, made up of 192, 1-dimensional lines, made up of 384, 0 dimension points.