One of the simplest multi-dimensional

structures is the four-dimensional
analogue

of an ordinary cube.

A theory of space as multi-dimensional

structure includes physical dimensions beyond

the three "spatial" and one "temporal"

including
gravity and other phenomena

as spatial dimensions.

A hypercube cannot be visualized

but one can unravel a hypercube

into its lower components

of ordinary 3D cubes (tesseract)

or to visualize its shadow-projections

or cross sections

The shadow of a cube

a square within a square.

The shadow of a hypercube

a cube within a cube.

The hypercube model is used as a communication structure

in parallel computing and complex information management

Engineers are constantly dealing with mathematical
structures using the square root of minus 1, which has a mathematical identity defining a 90 degree deviation
from "normal space", intrinsic to the mechanics of electro-magnetic
phenomena.
Mathematicians deal with multidimensional cosmology, or
hyperspace, by assigning most of the phenomena as physical dimensions, which are mutually orthogonal to each other, electric, magnetic and gravitic flux as dimensional manifestations.