This is sort of the basis of a visual model I have designed for a 4 cube/tesseract (what I call the "kaluza-klein cube" or "holocube") and a 5 cube (I call the "holofractal cube").

Holocube/Kaluza-Klein Cube: https://www.dropbox.com/s/3o0ovqe41j624wy/image4.jpeg?dl=0

Holo-Fractal Cube: https://www.dropbox.com/s/gmk375cgu2rylcu/image1.jpeg?dl=0

Although Kaluza-Klein theory has been disproven, I can't help but be amazed that solving Einstein's equations in the higher dimensions independently results the equations for electro-magnetism (light). I also can't help but like the idea quatum mechanics is simply physics for higher dimensions, and that all objects we believe are 3D extend both inward into 4D (particles) and outward from the object in 4D (light/electro-magnetism).

Edit: May be more accurate to say solving Einstein equations in 5th dimension independently yield the five-dimensional Einstein equations yield the four-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field.