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Nov 12 at 4:35 comment added Anton @IosifPinelis, in the setting I'm interested $P$ is not just convex, but also equiangular. Regardless, the answer given below asserts that this conjecture is false. I wonder if it would hold true should we impose both convexity and equiangularity.
Nov 12 at 4:31 history edited Anton CC BY-SA 4.0
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Nov 12 at 0:16 vote accept Anton
Nov 11 at 23:20 answer added user527492 timeline score: 5
Nov 11 at 22:30 history edited YCor CC BY-SA 4.0
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Nov 11 at 21:39 comment added Iosif Pinelis Is the polygon convex? Without this condition, your conjecture will not hold.
Nov 11 at 16:50 history asked Anton CC BY-SA 4.0