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This question already has an answer here:

If it's flat then how a volume can be flat? And I've read that it's actually not flat .....it's a "Poincaré dodecahedral space". Any suggestions for books posts or articles are highly appreciated.

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marked as duplicate by Qmechanic May 14 at 4:47

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  • $\begingroup$ “Flat” doesn’t mean flat like a piece of paper. It means “no spatial curvature”. There is no compelling evidence to support the Poincaré dodecahedral space idea. $\endgroup$ – G. Smith May 14 at 4:48
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    $\begingroup$ “As of 2016, the publication of data analysis from the Planck spacecraft suggests that there is no observable non-trivial topology to the universe.” (en.wikipedia.org/wiki/Homology_sphere) What you read is out-of-date. $\endgroup$ – G. Smith May 14 at 5:32