Point (0D) → line segment (1D) → square (2D) → cube (3D)... Push this pattern one step further and you get a tesseract (4D cube). We cannot see four dimensions directly, but just as the shadow of a cube is 2D, a tesseract can be projected as a “shadow” into 3D (or onto a 2D screen) so we can visualize it.
Find the pattern: A cube is made by connecting two squares (front and back) at their corresponding vertices. A tesseract is made in exactly the same way by connecting two cubes (inner and outer). Can you see the lines connecting the inner cube and the outer cube in the figure below?
XW plane rotation0°
YZ plane rotation0°
💡 In 4D space, rotation can happen in unfamiliar directions, such as the “XW plane,” which does not fit our usual 3D intuition. That is why this animation can make one cube appear to “pass through” another cube. This is not an optical illusion; it is a natural result of projecting a 4D rotation into 3D (and ultimately onto a 2D screen).