Finally some good results. I’ve used the hypertorus IGO to search the P2 plane group for the optimal packing of the of regular pentagons. The density found by the first run of the algorithm was 0.921310671743827. The optimal packing of regular pentagons proved by Hales and Kusner is ~0.921310674166737 ( https://milotorda.net/index.php/plane-group-packings-with-regular-pentagons/ ). The minimum distance between the pentagons in the packing is 3.937183912228193e-11. The algorithm can refine this just needs to run longer.
Left: Found configuration; Right: Zoom of the configuration
