To get from 2D space to 3D space using prisms, we multiply 'a' (Area of Face) by 'd' (Depth of 3D object). This literally expands out integeric value from 2D to 3D.

So what about 4D? Could we not simply multiply out again? Unfortunately we're not allowed to multiply out objects, only our integers.

Let's say we're looking at what I call a litre-cube. This is literally a cube with the correct dimensions (exactly 10cm X 10cm X 10cm) to hold no-more-no-less than a litre of water. This is also equivilent to 1KG of water, which is why I love the metric system.

Now, if I turn this into a 10cm X 10cm X 10cm X 10cm  cube, what the hell happens? Nothing, visually, but according to This, I'm ablse to flip this shit like anything as long as it keeps it's volume.

What about 5D, 6D 7D? a 10cm^7 cube would be able to shift through visual and none-visual dimensions! We could have 50 different desk layouts of which we can swap between at the push of a button, the flick of a switch, the click of a widget or the snap of a finger! Imagine being able to throw whatever you want around your room and simply flick a switch and have a machine with a 7D cable hooked up to it cleaning the rooms! We could clean the whole house with the flick of a button and whenever we bring something new in we need just register it if we want it to move!

Hereby, in the sci-fi story that I have half a plotline idea for, I'm gonna put multi-dimensional space into play.

[EDIT]

WOW.

What if there are things that we shouldn't see? What if in the Nth dimension there's things that the human brain can't comprehend? It works in with religion too - what if god gave us eyes only able to see what need be seen because any more would be dangerous and any less would be degrading? What's ju~st right, Goldie Locks?