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?
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2$\begingroup$ What is the question, exactly? $\endgroup$– Pietro MajerCommented Apr 16, 2019 at 18:53
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3$\begingroup$ 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 QuasCommented Apr 16, 2019 at 23:04
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2$\begingroup$ The Borsuk conjecture on centrally symmetric convex sets only guarantees pieces with smaller diameter, not similar figures. $\endgroup$– LeechLatticeCommented Apr 17, 2019 at 0:09
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