Since Borsuk conjecture hold for centrally symmetric convex sets in $\mathbb{R}^n$ so we can cut a hypercube into at least $n+1$ disjoint parts.

Is there a method how can one do that?


closed as off-topic by user44191, Sean Lawton, Jan-Christoph Schlage-Puchta, Pace Nielsen, Sebastian Goette Apr 17 at 15:45

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    $\begingroup$ What is the question, exactly? $\endgroup$ – Pietro Majer Apr 16 at 18:53
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    $\begingroup$ If $[-1,1]^n$ is decomposed into $[-1,0]\times[-1,1]^{n-1}$ and $(0,1]\times [-1,1]^{n-1}$, then the two pieces have diameter $2\sqrt{n-\frac 34}$ while the hypercube has diameter $2\sqrt n$, showing that the hypercube is not a counterexample. $\endgroup$ – Anthony Quas Apr 16 at 23:04
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    $\begingroup$ The Borsuk conjecture on centrally symmetric convex sets only guarantees pieces with smaller diameter, not similar figures. $\endgroup$ – Bullet51 Apr 17 at 0:09