Scalloped Ashtray 6¾" circa 1955-1956, Turquoise Green Decorated glaze, photos courtesy Jamie Heraver on Facebook's Marketplace

Notes:

1. The above information is for R-1568-S as R-1568 has not been found in a catalog and they are assumed to be the same design. An example marked R-1568-S is not known.
2. The brass insert shown in the below image from the 1956 Catalog is missing in the above photo.

Bottom reads:  ROYAL HAEGER R1568