3D projection of 4D "Octacube". ∞
A rather amazing sculpture, the subject of which is somewhat difficult to grasp, has been designed by Professor Ocneanu. It is a 3-diminsional representation, or shadow, of a 4-dimensional shape. More details at Science News Daily.
Another such four dimensional shape, which is perhaps easier to work out, is the tesseract. This is a 3D representation of the 4D shape, in the same way that a cube can be made from 6 squares laid out on a flat sheet of cardboard.
The human mind can’t generally work with more than 3 spatial dimensions (certainly I find it difficult), but mathematics shows that it is possible.
Whether this has any real use beyond art, I couldn’t say. But prof. Ocneanu’s sculpture certainly looks stunning from the photo, and I am sure it is more impressive in real life.