Here's a website that helps visualize 4 dimensional space! Although it does not exactly help to show the shape of the universe, it does show the nature of the universe. It also helps to describe the expansion of the universe with the use of the scale of time! Here's an image to show what I mean:
Despite the idea of the universe being in 4 dimensions, there are other theories out there that place the dimension of the universe at above 10 dimensions or more. One of these theories is called M-Theory, or also known as string theory. Popularly known as Sheldon Cooper of Big Bang Theory's field of study. M-theory dictates that the universe actually has 11 dimensions. For those who want to read on M-theory and its implications, check out these two websites!
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