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Jun 20, 2018 at 1:51 history edited Wlodek Kuperberg CC BY-SA 4.0
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Jun 19, 2018 at 1:05 comment added Wlod AA If I am right then there are counter-examples in all dimensions $\ n>1$ (similar to the one in dimension $2$; it'd take more writing though).
Jun 19, 2018 at 1:03 vote accept Wlodek Kuperberg
Jun 19, 2018 at 0:50 answer added Wlod AA timeline score: 7
Jun 19, 2018 at 0:41 comment added Wlodek Kuperberg @GerhardPaseman, Yeah, there may be a counterexample in $\mathbb{R}^3$ already.
Jun 19, 2018 at 0:17 comment added Gerhard Paseman It might be more revealing to consider two congruent convex bodies glued together on a common shaped face. The merged body may not seem as symmetric if an appropriate twist is given before gluing. Gerhard "Even If One Maintains Convexity" Paseman, 2018.06.18.
Jun 19, 2018 at 0:01 history asked Wlodek Kuperberg CC BY-SA 4.0