We can recreate a 3-dimensional picture on a 2-dimensional surface. Why can’t we visualize a 4-dimensional world in a 3-dimensional area?
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Our entire visual system works by representing a 3D world in 2D, so it’s very intuitive to do this for pictures. As other comments have stated, there are equivalents in higher dimensions, but they’re not nearly as intuitive for us to grasp.
The only reason we can properly understand the 2D representation of a 3D object is because we live in a 3D world, so we have a reference point. We’ve never experienced 4D.
That doesn’t stop us from trying though. If you google tesseract you’ll find 3D representations of a 4D object (or, rather 2D representations of the 3D representations, since you’re looking at a 2D screen).
We can. Just how like we can draw a cube (a 3D object) onto a piece of paper (a 2D plane), we can project a 4D object into 3D space. Here’s what a 4D cube (sometimes called a Tesseract) looks like projected in 3D space:
https://en.wikipedia.org/wiki/Tesseract
Just like when we project a cube onto a 2D piece of paper, we lose part of the shape by the projection. We can’t draw a cube that has angles that are all 90 degrees on a 2D piece of paper. Some angles will be skewed. Similarly, the angles between the sides of the tesseract are all actually 90 degrees, but only appear skewed when projected in 3D
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