what the 3d representation of a tesseract is actually showing
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The shadow of a 4D cube analog as cast onto a 3D surface.
It behaves in the same way as if you were to make a wire-frame cube and look at its 2D shadow. You know that the cubes sides are all squares. But the shadow does not show squares, it shows quadrilaterals with lengths and angles that change as you rotate the wire frame, as well as them going through eachother.
You have enough experience with cubes and shadows though, that you are able to infer the shape of the 3D object from its shadow. You are not able to do the same with a 4D object.
The 3D render shows you warped cubes (the “sides” of the 4D object), changing in size and angles, as the 4D object is rotated. These also go “through” eachother in the render.
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