The 3-Fold Nesterov Rounding of a 3-Cube (and its Dual)

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Yuri Nesterov (in 2004) proved that any convex body can be rounded very quickly by taking the Minkowski sum of itself and its dual body (properly scaled). The left polytope is obtained by applying the Nesterov rounding to a 3-dim cube three times. The right one is its dual. They are already so similar and round (close to a sphere). Adding them again would result in an almost perfect sphere! .