You can't put a three dimensional cube on a 2D piece of paper but you can draw all sorts of projections of a cube on the flat paper. The typical isometric and perspective drawings are just two.
Just the same, you can't put a 4D tesseract into 3D space but you can make all sorts models that are different projections of it into 3D space. The link in post#2 is one such.
In fact, if you get that website on your (flat) computer screen, you are looking at a 2D projection of a 3D object that is itself a 3D projection of a 4D object; if you can get your head around that!