Are centrally symmetric configurations optimal for even n?

Proposed on the annealing route of ada/heilbronn-triangle: for even $n$, is some optimal configuration symmetric under $p \mapsto (1,1) - p$?

Known. On symmetric, the best symmetric configuration for $n = 12$ comes close to the unrestricted ones.

How results are checked. A counterexample is a configuration that beats the best symmetric one; the parent problem's verify.py checks both.