PG packings of non centrally symmetric polygons with 3-fold rotational symmetry

We know that densest p1 configurations are lower or equal to general densest configurations. According to http://www.milotorda.net/index.php/packings/ p2, p2gg and pg densest packings of regular convex polygons coincide except for non centrally symmetric n-gons with a 3-fold rotational symmetry. Given densest pg packing configuration it is possible to construct p2 and p2gg packings with exactly same packing density as pg only by taking the same pg configuration and applying p2 and p2gg symmetry operations. This would mean that for regular polygons densest pg configurations are  lower or equal to densest p2gg and p2 configurations.

Below are p2gg and p2 packings of 9-gon, 21-gon and 39-gon based on respective densest pg packing configurations, although densest p2 and p2gg packings of 9, 21 and 39 gons are different.  From left to right: pg, p2gg and p2

9-gon with density 0.8986088

21-gon with density 0.9052376

39-gon with density 0.9064117