Kakutani's theorem is a result in geometry named after Shizuo Kakutani.
It states that every convex body in 3-dimensional space has a circumscribed cube, i.e. a cube all of whose faces touch the body.
[1] The result was further generalized by Yamabe and Yujobô to higher dimensions,[2] and by Floyd to other circumscribed parallelepipeds.
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