The 3-sphere is a surface of a 4D sphere, and is thus 3 dimensional. Then we should be able to look at it in our 3 dimensions. So what does it look like? Is it just a solid, 'filled-in' 3 dimensional sphere? If so, why doesn't Wikipedia just say that, instead of their convoluted explanation/photo 'stack of 3d spheres'? No mathematical jargon please.
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$\begingroup$A 3-sphere cannot fit into 3-dimensional euclidean space, just as a 2-sphere cannot be cut from a piece of paper. So while you can't just "look at it", here are two nice visualizations of what it would look like being inside the 3-sphere:
Spherical Geometry Is Stranger Than Hyperbolic - Hyperbolica Devlog #2
Spherical Space Building Game (Non-Euclidean Minecraft)
Interactive visualizations of 3-spheres, among other things, are available in your browser (3-dimensional.space) or downloadable (Curved Spaces).
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