Terrasects and the fourth-dimension

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Benito12
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I just learned about terrasects and the 4th-Dimension, I would like to know how you can make a terrasect on paper.(If it's possible)
 
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The text on that page isn't very clear but my understanding is that the diagram is not of a tesseract but of its three dimensional shadow.
 
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!