If you are confused, here is how I understand it best:

(Spoilerized for space reasons, if tl;dr then you can skip but not my fault if you don't understand other stuff)

If you're having trouble picturing n-dimensional objects, start by imagining a single geometric point.

A 1D point can be referenced like so: (X)

A 2D point is referenced like this: (X,Y)

While a 3D point is like this: (X,Y,Z)

And a n-D point is like this (a1,a2,a3...an)

Now, imagine seperate each of those numbers.

A 1D point (X) can be represented on a number line.

Next add another number line for Y, this is 2-dimensional.

You can continue the process for n-dimensions

A single n-D point has one position on each of these dimensions.

Now onto solids!

I'm going to spend a little less time on this because I'm starting to confuse myself,

but here it is:

Start with a box. It has length width and height.

If you take the box and cut out one of the dimensions, you have an infinite array of 2D squares.

If you cut a second dimension out, you have an infinite number of line segments.

These are all solids.

Wait a sec? Line segments! Those could go on a -number line-.

3 line segments could represent the box's dimensions in height length and width!

*Drumroll please*

A 3D box can be visualized like this-

`0--------[XXXX]-0`

0----[XXXX]-----0

0------[XXXX]---0

And you can add infinite dimensions the same way, an n-D point is always a point on each line, a segment on each line is always a solid.

`Points A and B in 8 dimensions (when they're in the same position they're shown on top of each other)`

0-A--B0 0--B-A0

0-B-A-0 0--A--0

B

0-A---0 0-B-A-0

B

0B-A--0 0-A-B-0

(it might get hard to do with large numbers of objects coinciding on the same position on one line,

but I still think it's better than silly multiple 3D image nonsense)

In game you could have each axis centered on the character

and only show things within a certain distance on each dimension, like the origin on a number line.

That way moving to a position is as easy as sliding along each axis until you're at the same point.

If you run into something then that would be the puzzle part of the game.

`2D example and conversion to lines, X is the player, Y is the target, @ is the obstruction`

-----

--Y--

--@--

--X--

-----

(V)<=Obstruction

(D1)0--X--0 (D2)0--X@Y0

@

Y

The character would have to be moved on other dimensions until you can get around it.

Reverting to base 2 when doing math with hexadecimal is a similar process.

Higher bases are generally hard to understand, so are higher dimensions.

That means you have to revert to 1D and solve.