I think other posters have done a good job explaining conceptually what a Tesseract it, but maybe you’re also wondering what [these well know 3D tesseract models are](https://media.printables.com/media/prints/146580/images/1383071_9e6af9d4-08d9-4d1a-a9d8-e3ef93b5b503/thumbs/inside/1280×960/jpg/88693291339c588951373115531ede4a_display_large_14.webp)?
Well, in our 3D space shadows are 2D right? So if you imagine holding a hollow cube up to the light [it would make a shadow like this](https://i.stack.imgur.com/A3rfx.png).
In 4D space shadows are 3D! So if you held a hollow tesseract up to the light in 4D space the shadow would be that 3D model of a tesseract.
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