Configurations exceeding the 25n/7 equilibrium threshold

Construct a configuration of n unit point charges in R^3 whose electrostatic potential has more than 25n/7 equilibria.

Background

The authors construct iterated square anti-prism configurations whose ratio of equilibria to point charges approaches 25/7 from below. This establishes a record for the number of equilibria per charge within their constructions, but does not show that 25/7 is optimal.

They explicitly ask whether another configuration can surpass the resulting threshold.

References

Can one find an example of a configuration of $n$ unit point changes in $R3$ whose electrostatic potential has a number of equilibria that exceeds $\sfrac{25 n}{7}$?

— Counting Equilibria of the Electrostatic Potential  (2501.05315 - Edelsbrunner et al., 9 Jan 2025) in Question following Section 2.4, Section 2