I agree with the Turkoman attribution, and the suggestion that it is a "recycled" item.
The central beadwork hexagon is very reminiscent of the gul design forms that are featured on Turokoman carpets and bag faces, but I've never seen anything like it in any older piece, leading me to believe that it is of more recent construction, harking back to the traditional designs.
Link to carpet gul images:
https://www.google.com/search?q=carp...HSXIB-wQsAQIRA