A 3d represntation of a 4 dimensional cube The formula to create one of these is actually very simple, or I should to create an X dimensional one.
In simple terms a 2 dimensional cube is a square and how you do it is to draw a single line (calli it segment 1) and call its base Point 0 draw another line that is 90 degrees (call this one segment 2) to the original so it originates from Point 0, then move to the end of a given segment and figure out which segments have not be drawn yet at the end of the segment you are currently on.
So for starting on segment one and going from point 0 up to the end of that segment you have not drawn segment 2 so go ahead and draw it then go back to point 0 and go down the first segment 2 to its end and the only segment you have not drawn on that path is segment one so draw it.
so here how it works in shorthand
start at point zero
draw segment 1 vertically
go back to point zero
draw new segment 90 degrees from first segment this is segment 2
you should have an "L" shape
now go back to Point 0 and move along the path of segment one to its end and since on this path youhave only drawn segment 1 now draw teh missing segment, segment 2, here.
Now you should have a "C" shape
Go back to point 0 since all the segments are now drawn on the first path we checked go to the other path, the first segment 2 you drew.starting at point 0 move along segment 2 to its end and draw teh remaining segment you haven't drawn on this path which is segment 1.
you should now have a squareor a two dimensional cube.
Now here is where your mind comes into play everyone has seen the 3 dimensional wire drawing of a cube and we all know that the diagonal line is to be assumed at a 90 degree angle from theother two line just in perspective the same is done here to go into higher dimensional cubes
For each direction a new line segment is added each to be assumed is at 90 degree from the others that si wher our mind has to leap to but the methodology remains exactly the same.
The first two lines are easily seen as 90 degree off from eachother the others are not and that makes drawing them tricky actually modleing them on a computer is much fast and easier,
So enjoy this one and once printed put it on a slowing spinning platdorm and it will be neat to watch
Added one pic to show it with supports
I printed this in PLA at 200 microns at full size so it is 4.25 x 4.25 x 5 not quite a square but close and I used supports and it took a long time 34 hours at my speed and it had a LOT of support but it turned out great I have also printed ones at have size without support and they were much faster but some looping of the lines did occur