A tesseract can be represented in normal 3D space, but it’s labelled a 4D object – why is this?
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Imagine holding up a wireframe of a cube to the light so it casts a shadow. That shadow might look like [this](https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcR22utzNY-yTYMfzwEhGbi8W02kSGVy1o-8YojjDo9a2kYXv79Xb_BFrJJyvRQf8KrlQe0&usqp=CAU). Rotate it another way and you might get [this](https://www.researchgate.net/profile/Nicole-Panorkou/publication/307617685/figure/fig12/AS:402998749614091@1473093797815/A-cube-or-a-hexagon.png) depending on the angle you hold it. The 3D cube casts a 2D shadow. In math they call this a projection.
The tesseracts you see aren’t a 4D shape because we can’t see in 4 spatial dimensions at once. The closest we can get to representing one visually is a projection. So when you are looking at [this projection of rotating tesseract](https://www.youtube.com/watch?v=g8ypKnaC3xA), you are looking at the shadow a 4D tesseract would cast onto 3D space.
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