CM to P2MG packings

Same thing as for the PG group ( can be done for the CM group. At least for regular convex polygons. That is, given a CM packing one construct a P2MG packing with exactly same density, fairly easily. For most of regular polygons CM a P2MG packings have the same densities. The exceptions are regular convex polygons with 12k-1 and 12k+1 rotational symmetries. See:

Below are some examples of densest CM packings converted to P2MG packings. The P2MG packings are not the densest P2MG packings in these instances. From left to right: CM and P2MG

11-gon with density 0.8279530

13-gon with density 0.8321287

23-gon with density 0.8386501