A 4th Dimensional Hypercube I created! All joints should fit in correctly/easily, and they do snap in. However, if you want a model you can easily pull apart, I suggest shrinking the dimensions of the cylinders proportionately by 97%, leaving all joint-connecters alone. 

As I understand it, the 4th dimension has 8 directions, two more than that of the third. When a cube is put faceup in one of the six directions it has (up, down, left, right), it will look as if it is a square (the second dimension). When looking at this model, You can tilt it in any of the 8 solid directions it has to make the illusion of a cube (the third dimension). You can see this same illusion on the same model 8 different times, and if you want to see it easier, try looking at the shadow the object makes. You can even make the model show two cubes (one stacked on top of the other) if you turn it correctly. This is equivalent to you seeing two squares on a cube (they'll look more like rectangles and be connected by a line (intersection of two planes)). And lastly, if you turn it just right you can find what seems to be three rectangular 3d objects each stacked on top of one another in a row. This is equivalent to a cube if you had it as a solid, and you turned it so that you could see three faces. Thanks for reading!