I’ve searched the P1 group to find the densest packing of regular octagons since since the densest packing of convex set with central symmetry in the plane is a lattice packing ie a member of P1 plane group. The density I found is 0.906163653094707. The analytical result for the optimal density is ~ 0.906163678643946. ( Packing Regular Octagons ). The minimum distance between the octagons in the packing is 1.950763550695456e-09.
Left: Found configuration; Right: Zoom of the configuration
