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Claim. Tao Hu and Quanyu Tang, Counterexamples for Problem #1045 (version 1.0, 3 October 2025), exhibit the kite $\{(0,0),(\sqrt3,1),(\sqrt3,-1),(2,0)\}$, whose ordered product $4096(7-4\sqrt3)\approx294.08$ exceeds the square's $256$, and an explicit six-point set of diameter $2$, given in eight-decimal coordinates and checked by computer, whose ordered product is about $47920.8$, above the regular hexagon's $6^6=46656$. So the regular polygon does not maximize the product of Problem 1045 at $n=4$ or $n=6$. The note reports numerical evidence that the regular pentagon is optimal at $n=5$ and makes no claim for odd $n$.

Covers. A negative answer to the regular-polygon question at $n=4$ and $n=6$. Both cases were already settled by Danzer and Pommerenke in 1967.

Depends on. No page of this wiki.

Standing. A note posted on GitHub and linked from the site's thread on 3 October 2025; it has no journal publication. The site's commentary credits the examples, but the site labels the problem OPEN, so the credit is not review.