I’ve been trying to get a better solution to the heptagon packing in P2 than previously( https://milotorda.net/index.php/packing-of-regular-heptagons-in-the-p2-group-using-the-hypertorus-igo/ ) and I did. It just take long. The decay of the neighbourhoods has to be very slow ie. 1/1.25. The density of the structure is 0.892690680150324.
Left: Found configuration; Right: Zoom of the configuration
